Osaka Journal of Mathematics Articles (Project Euclid)
http://projecteuclid.org/euclid.ojm
The latest articles from Osaka Journal of Mathematics on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2010 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Thu, 05 Aug 2010 15:41 EDTTue, 22 Mar 2011 10:05 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
http://projecteuclid.org/
Quotients of bounded homogeneous domains by cyclic groups
http://projecteuclid.org/euclid.ojm/1277298908
<strong>Christian Miebach</strong><p><strong>Source: </strong>Osaka J. Math., Volume 47, Number 2, 331--352.</p><p><strong>Abstract:</strong><br/>
Let $D$ be a bounded homogeneous domain in $\mathbb{C}^{n}$
and let $\varphi$ be an automorphism of $D$ which generates
a discrete subgroup $\Gamma$ of $\Aut_{\mathcal{O}}(D)$. It
is shown that the complex space $D/\Gamma$ is Stein.
</p>projecteuclid.org/euclid.ojm/1277298908_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTOn the spectral Hausdorff dimension of 1D discrete Schrödinger operators under power decaying perturbationshttp://projecteuclid.org/euclid.ojm/1496282424<strong>V.R. Bazao</strong>, <strong>S.L. Carvalho</strong>, <strong>C.R. de Oliveira</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 2, 273--285.</p><p><strong>Abstract:</strong><br/>
We show that spectral Hausdorff dimensional properties of discrete Schrödinger operators with (1) Sturmian potentials of bounded density and (2) a class of sparse potentials are preserved under suitable polynomial decaying perturbations, when the spectrum of these perturbed operators have some singular continuous component.
</p>projecteuclid.org/euclid.ojm/1496282424_20170531220031Wed, 31 May 2017 22:00 EDTScattering for quasilinear hyperbolic equations of Kirchhoff type with perturbationhttp://projecteuclid.org/euclid.ojm/1496282425<strong>Taeko Yamazaki</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 2, 287--322.</p><p><strong>Abstract:</strong><br/>
This paper is concerned with the abstract quasilinear hyperbolic equations of Kirchhoff type with perturbation. We show the existence of the wave operators and the scattering operator for small data, and that these operators are homeomorphic with respect to a suitable metric in a neighborhood of the origin.
</p>projecteuclid.org/euclid.ojm/1496282425_20170531220031Wed, 31 May 2017 22:00 EDTOn two moduli spaces of sheaves supported on quadric surfaceshttp://projecteuclid.org/euclid.ojm/1496282426<strong>Mario Maican</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 2, 323--333.</p><p><strong>Abstract:</strong><br/>
We show that the moduli space of semi-stable sheaves on a smooth quadric surface, having dimension $1$, multiplicity $4$, Euler characteristic $2$, and first Chern class $(2, 2)$, is the blow-up at two points of a certain hypersurface in a weighted projective space.
</p>projecteuclid.org/euclid.ojm/1496282426_20170531220031Wed, 31 May 2017 22:00 EDTA generalization of Nakai's theorem on locally finite iterative higher derivationshttp://projecteuclid.org/euclid.ojm/1496282427<strong>Shigeru Kuroda</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 2, 335--341.</p><p><strong>Abstract:</strong><br/>
Let $k$ be a field of arbitrary characteristic. In 1978, Nakai proved a structure theorem for $k$-domains admitting a nontrivial locally finite iterative higher derivation when $k$ is algebraically closed. In this paper, we generalize Nakai's theorem to cover the case where $k$ is not algebraically closed. As a consequence, we obtain a cancellation theorem of the following form: Let $A$ and $A'$ be finitely generated $k$-domains with $A[x]\simeq _kA'[x]$. If $A$ and $\bar{k}\otimes _kA$ are UFDs and $\mathop{\rm trans.deg}\nolimits _kA=2$, then we have $A\simeq _kA'$. This generalizes the cancellation theorem of Crachiola.
</p>projecteuclid.org/euclid.ojm/1496282427_20170531220031Wed, 31 May 2017 22:00 EDT$p$-local stable cohomological rigidity of quasitoric manifoldshttp://projecteuclid.org/euclid.ojm/1496282428<strong>Sho Hasui</strong>, <strong>Daisuke Kishimoto</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 2, 343--350.</p><p><strong>Abstract:</strong><br/>
It is proved that if two quasitoric manifolds of dimension $\le 2p^2-4$ for a prime $p$ have isomorphic cohomology rings, then they have the same $p$-local stable homotopy type.
</p>projecteuclid.org/euclid.ojm/1496282428_20170531220031Wed, 31 May 2017 22:00 EDTFree product of two elliptic quaternionic Möbius transformationshttp://projecteuclid.org/euclid.ojm/1496282429<strong>Wensheng Cao</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 2, 351--362.</p><p><strong>Abstract:</strong><br/>
Suppose that $f$ and $g$ are two elliptic quaternionic Möbius transformations of orders $m$ and $n$ respectively. If the hyperbolic distance $\delta(f,g)$ between ${\rm fix}(f)$ and ${\rm fix}(g)$ satisfies $$\cosh \delta(f,g) \geq\frac{\cos\frac{\pi}{m}\cos\frac{\pi}{n}+1}{\sin\frac{\pi}{m}\sin\frac{\pi}{n}},$$ then the group $\langle f , g\rangle$ is discrete non-elementary and isomorphic to the free product $\langle f \rangle* \langle g\rangle$.
</p>projecteuclid.org/euclid.ojm/1496282429_20170531220031Wed, 31 May 2017 22:00 EDTPretzel Knots and $q$-Serieshttp://projecteuclid.org/euclid.ojm/1496282430<strong>Mohamed Elhamdadi</strong>, <strong>Mustafa Hajij</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 2, 363--381.</p><p><strong>Abstract:</strong><br/>
The tail of the colored Jones polynomial of an alternating link is a $q$-series invariant whose first $n$ terms coincide with the first $n$ terms of the $n$-th colored Jones polynomial. Recently, it has been shown that the tail of the colored Jones polynomial of torus knots give rise to Ramanujan type identities. In this paper, we study $q$-series identities coming from the colored Jones polynomial of pretzel knots. We prove a false theta function identity that goes back to Ramanujan and we give a natural generalization of this identity using the tail of the colored Jones polynomial of Pretzel knots. Furthermore, we compute the tail for an infinite family of Pretzel knots and relate it to false theta function-type identities.
</p>projecteuclid.org/euclid.ojm/1496282430_20170531220031Wed, 31 May 2017 22:00 EDTOn the Gevrey strong hyperbolicityhttp://projecteuclid.org/euclid.ojm/1496282431<strong>Tatsuo Nishitani</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 2, 383--408.</p><p><strong>Abstract:</strong><br/>
In this paper we are concerned with a homogeneous differential operator $p$ of order $m$ of which characteristic set of order $m$ is assumed to be a smooth manifold. We define the Gevrey strong hyperbolicity index as the largest number $s$ such that the Cauchy problem for $p+Q$ is well-posed in the Gevrey class of order $s$ for any differential operator $Q$ of order less than $m$. We study the case of the largest index and we discuss in which way the Gevrey strong hyperbolicity index relates with the geometry of bicharacteristics of $p$ near the characteristic manifold.
</p>projecteuclid.org/euclid.ojm/1496282431_20170531220031Wed, 31 May 2017 22:00 EDTMori Dream Spaces extremal contractions of K3 surfaceshttp://projecteuclid.org/euclid.ojm/1502092821<strong>Alice Garbagnati</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 3, 409--433.</p><p><strong>Abstract:</strong><br/>
We will give a criterion to assure that an extremal contraction of a K3 surface which is not a Mori Dream Space produces a singular surface which is a Mori Dream Space. We list the possible Néron--Severi groups of K3 surfaces with this property and an extra geometric condition such that the Picard number is greater than or equal to 10. We give a detailed description of two geometric examples for which the Picard number of the K3 surface is 3, i.e. the minimal possible in order to have the required property. Moreover we observe that there are infinitely many examples of K3 surfaces with the required property and Picard number equal to 3.
</p>projecteuclid.org/euclid.ojm/1502092821_20170807040038Mon, 07 Aug 2017 04:00 EDTWeak convergence of regular Dirichlet subspaceshttp://projecteuclid.org/euclid.ojm/1502092822<strong>Liping Li*</strong>, <strong>Toshihiro Uemura</strong>, <strong>Jiangang Ying**</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 3, 435--455.</p><p><strong>Abstract:</strong><br/>
In this paper we shall prove the weak convergence of the associated diffusion processes of regular subspaces with monotone characteristic sets for a fixed Dirichlet form. More precisely, given a fixed 1-dimensional diffusion process and a sequence of its regular subspaces, if the characteristic sets of regular subspaces are decreasing or increasing, then their associated diffusion processes are weakly convergent to another diffusion process. This is an extended result of [14].
</p>projecteuclid.org/euclid.ojm/1502092822_20170807040038Mon, 07 Aug 2017 04:00 EDTA finite generating set for the level 2 twist subgroup of the mapping class group of a closed non-orientable surfacehttp://projecteuclid.org/euclid.ojm/1502092823<strong>Ryoma Kobayashi</strong>, <strong>Genki Omori</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 3, 457--474.</p><p><strong>Abstract:</strong><br/>
We obtain a finite generating set for the level 2 twist subgroup of the mapping class group of a closed non-orientable surface. The generating set consists of crosscap pushing maps along non-separating two-sided simple loops and squares of Dehn twists along non-separating two-sided simple closed curves. We also prove that the level 2 twist subgroup is normally generated in the mapping class group by a crosscap pushing map along a non-separating two-sided simple loop for genus $g\geq 5$ and $g=3$. As an application, we calculate the first homology group of the level 2 twist subgroup for genus $g\geq 5$ and $g=3$.
</p>projecteuclid.org/euclid.ojm/1502092823_20170807040038Mon, 07 Aug 2017 04:00 EDTCritical levels and Jacobi fields in a complex of cycleshttp://projecteuclid.org/euclid.ojm/1502092824<strong>Ingrid Irmer</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 3, 475--497.</p><p><strong>Abstract:</strong><br/>
In this paper it is shown that the space of tight geodesic segments connecting any two vertices in a complex of cycles has finite, uniformly bounded dimension. The dimension is defined in terms of a discrete analogue of Jacobi fields, which are explicitly constructed and shown to give a complete description of the entire space of tight geodesics. Jacobi fields measure the extent to which geodesic stability breaks down. Unlike most finiteness properties of curve complexes, the arguments presented here do not rely on hyperbolicity, but rather on structures similar to Morse theory.
</p>projecteuclid.org/euclid.ojm/1502092824_20170807040038Mon, 07 Aug 2017 04:00 EDTFeller evolution families and parabolic equations with form-bounded vector fieldshttp://projecteuclid.org/euclid.ojm/1502092825<strong>Damir Kinzebulatov</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 3, 499--516.</p><p><strong>Abstract:</strong><br/>
We show that the weak solutions of parabolic equation $\partial_t u - \Delta u + b(t,x) \cdot \nabla u=0$, $(t,x) \in (0,\infty) \times \mathbb R^d$, $d \geqslant 3$, for $b(t,x)$ in a wide class of time-dependent vector fields capturing critical order singularities, constitute a Feller evolution family and, thus, determine a Feller process. Our proof uses an a priori estimate on the $L^p$-norm of the gradient of solution in terms of the $L^q$-norm of the gradient of initial function, and an iterative procedure that moves the problem of convergence in $L^\infty$ to $L^p$.
</p>projecteuclid.org/euclid.ojm/1502092825_20170807040038Mon, 07 Aug 2017 04:00 EDTCompactness of Markov and Schrödinger semi-groups: A probabilistic approachhttp://projecteuclid.org/euclid.ojm/1502092826<strong>Masayoshi Takeda</strong>, <strong>Yoshihiro Tawara</strong>, <strong>Kaneharu Tsuchida</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 3, 517--532.</p><p><strong>Abstract:</strong><br/>
It is proved if an irreducible, strong Feller symmetric Markov process possesses a tightness property, then its semi-group is an $L^2$-compact operator. In this paper, applying this fact, we prove probabilistically the compactness of Dirichlet-Laplacians and Schrödinger operators.
</p>projecteuclid.org/euclid.ojm/1502092826_20170807040038Mon, 07 Aug 2017 04:00 EDTLie algebras constructed with Lie modules and their positively and negatively graded moduleshttp://projecteuclid.org/euclid.ojm/1502092827<strong>Nagatoshi Sasano</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 3, 533--568.</p><p><strong>Abstract:</strong><br/>
In this paper, we shall give a way to construct a graded Lie algebra $L(\mathfrak{g},\rho,V,{\cal V},B_0)$ from a standard pentad $(\mathfrak{g},\rho,V,{\cal V},B_0)$ which consists of a Lie algebra $\mathfrak{g}$ which has a non-degenerate invariant bilinear form $B_0$ and $\mathfrak{g}$-modules $(\rho, V)$ and ${\cal V}\subset \mathrm {Hom }(V,F)$ all defined over a field $F$ with characteristic $0$. In general, we do not assume that these objects are finite-dimensional. We can embed the objects $\mathfrak{g},\rho,V,{\cal V}$ into $L(\mathfrak{g},\rho,V,{\cal V},B_0)$. Moreover, we construct specific positively and negatively graded modules of $L(\mathfrak{g},\rho,V,{\cal V},B_0)$. Finally, we give a chain rule on the embedding rules of standard pentads.
</p>projecteuclid.org/euclid.ojm/1502092827_20170807040038Mon, 07 Aug 2017 04:00 EDTOn Jacobi forms of real weights and indiceshttp://projecteuclid.org/euclid.ojm/1502092828<strong>Hiroki Aoki</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 3, 569--585.</p><p><strong>Abstract:</strong><br/>
In this paper, we investigate weak Jacobi forms of real weights and indices, and show that they have a very simple structure theorem even when their weights and indices are not integral. By using this structure theorem, we can determine possible weights of Siegel paramodular forms.
</p>projecteuclid.org/euclid.ojm/1502092828_20170807040038Mon, 07 Aug 2017 04:00 EDTA twisted first homology group of the handlebody mapping class grouphttp://projecteuclid.org/euclid.ojm/1502092829<strong>Tomohiko Ishida</strong>, <strong>Masatoshi Sato</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 3, 587--619.</p><p><strong>Abstract:</strong><br/>
Let $H_g$ be a 3-dimensional handlebody of genus $g$. We determine the twisted first homology group of the mapping class group of $H_g$ with coefficients in the first integral homology group of the boundary surface $\partial H_g$ for $g\ge2$.
</p>projecteuclid.org/euclid.ojm/1502092829_20170807040038Mon, 07 Aug 2017 04:00 EDTCorrigendum to ``Deformations of special Legendrian submanifolds with boundary" Osaka J. Math. 51 (2014), 673--693http://projecteuclid.org/euclid.ojm/1502092830<strong>Guangcun Lu</strong>, <strong>Xiaomin Chen</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 3, 621--622.</p><p><strong>Abstract:</strong><br/>
</p>projecteuclid.org/euclid.ojm/1502092830_20170807040038Mon, 07 Aug 2017 04:00 EDTOrder of the canonical vector bundle over configuration spaces of projective spaceshttps://projecteuclid.org/euclid.ojm/1508486563<strong>Shiquan Ren</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 623--634.</p><p><strong>Abstract:</strong><br/>
The order of a vector bundle is the smallest positive integer $n$ such that the vector bundle's $n$-fold self-Whitney sum is trivial. Since 1970's, the order of the canonical vector bundle over configuration spaces of Euclidean spaces has been studied by F.R. Cohen, R.L. Cohen, N.J. Kuhn and J.L. Neisendorfer [4], F.R. Cohen, M.E. Mahowald and R.J. Milgram [6], and S.W. Yang [17, 18]. And the order of the canonical vector bundle over configuration spaces of closed orientable Riemann surfaces with genus greater than or equal to one has been studied by F.R. Cohen, R.L. Cohen, B. Mann and R.J. Milgram [5]. In this paper, we study the order of the canonical vector bundle over configuration spaces of projective spaces as well as of the Cartesian products of a projective space and a Euclidean space.
</p>projecteuclid.org/euclid.ojm/1508486563_20171020040335Fri, 20 Oct 2017 04:03 EDTCommensurability of link complementshttps://projecteuclid.org/euclid.ojm/1508486566<strong>Han Yoshida</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 635--645.</p><p><strong>Abstract:</strong><br/>
In 2013, Chesebro and DeBlois constructed a certain family of hyperbolic links whose complements have the same volume, trace field, Bloch invariant, and cusp parameters up to $PGL(2,\mathbb Q)$. In this paper, we show that these link complements are incommensurable to each other. We use horoball packing to prove this.
</p>projecteuclid.org/euclid.ojm/1508486566_20171020040335Fri, 20 Oct 2017 04:03 EDTEquivariant maps between representation spheres of cyclic ${p}$-groupshttps://projecteuclid.org/euclid.ojm/1508486569<strong>Ko Ohashi</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 647--659.</p><p><strong>Abstract:</strong><br/>
This paper deals with necessary conditions for the existence of equivariant maps between the unit spheres of unitary representations of a cyclic $p$-group $G$. T. Bartsch gave a necessary condition for some unitary representations of $G$ by using equivariant $K$-theory. We give two necessary conditions following Bartsch's approach. One is a generalization of Bartsch's result for any unitary representation of $G$ which does not contain the trivial representation. The other is a stronger necessary condition for some special cases.
</p>projecteuclid.org/euclid.ojm/1508486569_20171020040335Fri, 20 Oct 2017 04:03 EDTDECOMPOSITION OF COMPLEX HYPERBOLIC ISOMETRIES BY TWO COMPLEX SYMMETRIEShttps://projecteuclid.org/euclid.ojm/1508486570<strong>Xue-Jing Ren</strong>, <strong>Bao-Hua Xie</strong>, <strong>Yue-Ping Jiang</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 661--677.</p><p><strong>Abstract:</strong><br/>
Let $\mathbf{PU}(2,1)$ denote the holomorphic isometry group of the $2$-dimensional complex hyperbolic space $\mathbf{H}_{\mathbb{C}}^{2}$, and the group $\mathbf{SU}(2,1)$ is a 3-fold covering of $\mathbf{PU}(2,1)$: $\mathbf{PU}(2,1)=\mathbf{SU}(2,1)/\{\omega I:\omega^{3}=1\}$. We study how to decompose a given pair of isometries $(A,B)\in \mathbf{SU}(2,1)^{2}$ under the form $A=I_{1}I_{2}$ and $B=I_{3}I_{2},$ where the $I_{k}$'s are complex symmetries about complex lines. If $(A,B)$ can be written as above, we call it is $\mathbb{C}$-decomposable. The main results are decomposability criteria, which improve and supplement the result of [17].
</p>projecteuclid.org/euclid.ojm/1508486570_20171020040335Fri, 20 Oct 2017 04:03 EDTBranched twist spins and knot determinantshttps://projecteuclid.org/euclid.ojm/1508486572<strong>Mizuki Fukuda</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 679--688.</p><p><strong>Abstract:</strong><br/>
A branched twist spin is a generalization of twist spun knots, which appeared in the study of locally smooth circle actions on the $4$-sphere due to Montgomery, Yang, Fintushel and Pao. In this paper, we give a sufficient condition to distinguish non-equivalent, non-trivial branched twist spins by using knot determinants. To prove the assertion, we give a presentation of the fundamental group of the complement of a branched twist spin, which generalizes a presentation of Plotnick, calculate the first elementary ideals and obtain the condition of the knot determinants by substituting $-1$ for the indeterminate.
</p>projecteuclid.org/euclid.ojm/1508486572_20171020040335Fri, 20 Oct 2017 04:03 EDTOn a theorem of Muraihttps://projecteuclid.org/euclid.ojm/1508486573<strong>Gabriel Navarro</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 689--690.</p><p><strong>Abstract:</strong><br/>
If $B$ is a $p$-block of a finite group $G$, then the intersection of the kernels of the height zero characters in $B$ has a normal $p$-complement.
</p>projecteuclid.org/euclid.ojm/1508486573_20171020040335Fri, 20 Oct 2017 04:03 EDTLongtime convergence for epitaxial growth model under Dirichlet conditionshttps://projecteuclid.org/euclid.ojm/1508486574<strong>Somayyeh Azizi</strong>, <strong>Gianluca Mola</strong>, <strong>Atsushi Yagi</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 691--708.</p><p><strong>Abstract:</strong><br/>
This paper continues our study on the initial-boundary value problem for a semilinear parabolic equation of fourth order which has been presented by Johnson-Orme-Hunt-Graff-Sudijono-Sauder-Orr [12] to describe the large-scale features of a growing crystal surface under molecular beam epitaxy. In the preceding paper [1], we already constructed a dynamical system generated by the problem and verified that the dynamical system has a finite-dimensional attractor (especially, every trajectory has nonempty $\omega$-limit set) and admits a Lyapunov function (of the form (3.1)). This paper is then devoted to showing longtime convergence of trajectory. We shall prove that every trajectory converges to some stationary solution as $t \to \infty$. As a matter of fact, we have obtained in [10] the similar result for the equation but under the Neumann like boundary conditions $\frac{\partial u}{\partial n}=\frac\partial{\partial n}\varDelta u=0$ on the unknown function $u$. In this paper, we want as in [1] to handle the Dirichlet boundary conditions $u=\frac{\partial u}{\partial n}=0$, maybe physically more natural conditions than before.
</p>projecteuclid.org/euclid.ojm/1508486574_20171020040335Fri, 20 Oct 2017 04:03 EDTParabolic, ridge and sub-parabolic curves on implicit surfaces with singularitieshttps://projecteuclid.org/euclid.ojm/1508486575<strong>Masaru Hasegawa</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 709--723.</p><p><strong>Abstract:</strong><br/>
We study parabolic, ridge and sub-parabolic curves on implicit surfaces defined by smooth functions $\mathcal{R}$-equivalent to $A_1^-$-singularity. To investigate ridge and sub-parabolic curves, we present the local parameterizations of the implicit surfaces, and we show the asymptotic behavior of the principal curvatures and directions by using the parameterization. We also present height and distance squared functions on implicit surfaces in the appendix.
</p>projecteuclid.org/euclid.ojm/1508486575_20171020040335Fri, 20 Oct 2017 04:03 EDTOn the Morse-Novikov number for 2-Knotshttps://projecteuclid.org/euclid.ojm/1508486576<strong>Hisaaki Endo</strong>, <strong>Andrei Pajitnov</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 725--736.</p><p><strong>Abstract:</strong><br/>
Let $K\subset S^4$ be a 2-knot. The Morse-Novikov number ${\mathcal M}{\mathcal N}(K)$ is the minimal possible number of critical points of a Morse map $S^4\setminus K\to S^1$ belonging to the canonical class in $H^1(S^4\setminus K)$. We prove that for a classical knot $K\subset S^3$ the Morse-Novikov number of the spun knot $S(K)$ is $\leq 2{\mathcal M}{\mathcal N}(K)$. This enables us to compute ${\mathcal M}{\mathcal N}(S(K))$ for every classical knot $K$ with tunnel number 1.
</p>projecteuclid.org/euclid.ojm/1508486576_20171020040335Fri, 20 Oct 2017 04:03 EDTExtrinsic circular trajectories on geodesic spheres in a complex projective spacehttps://projecteuclid.org/euclid.ojm/1508486577<strong>Tuya Bao</strong>, <strong>Toshiaki Adachi</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 737--747.</p><p><strong>Abstract:</strong><br/>
We say a trajectory for a Sasakian magnetic field on a geodesic sphere in a complex projective space to be extrinsic circular if it can be seen as a circle in the ambient space. We study how the moduli space of extrinsic circular trajectories behaves in the moduli space of all circles in the ambient complex projective space. As an application we characterize the geodesic sphere of special radius which lies on the boundary position of the family of Berger spheres among all geodesic spheres and that has a characteristic properties from the viewpoint of lengths of circles.
</p>projecteuclid.org/euclid.ojm/1508486577_20171020040335Fri, 20 Oct 2017 04:03 EDTProperties of the Dirac spectrum on three dimensional lens spaceshttps://projecteuclid.org/euclid.ojm/1508486578<strong>Sebastian Boldt</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 749--767.</p><p><strong>Abstract:</strong><br/>
We present a spectral rigidity result for the Dirac operator on lens spaces. More specifically, we show that each homogeneous lens space and each three dimensional lens space $L(q;p)$ with $q$ prime is completely characterized by its Dirac spectrum in the class of all lens spaces.
</p>projecteuclid.org/euclid.ojm/1508486578_20171020040335Fri, 20 Oct 2017 04:03 EDTOn ramified torsion points on a curve with stable reduction over an absolutely unramified basehttps://projecteuclid.org/euclid.ojm/1508486579<strong>Yuichiro Hoshi</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 769--789.</p><p><strong>Abstract:</strong><br/>
Let $p$ be an odd prime number, $W$ an {\it absolutely unramified} $p$-adically complete discrete valuation ring with algebraically closed residue field, and $X$ a curve of genus at least two over the field of fractions $K$ of $W$. In the present paper, we study, under the assumption that $X$ has {\it stable reduction} over $W$, {\it torsion points} on $X$, i.e., torsion points of the Jacobian variety $J$ of $X$ which lie on the image of the Albanese embedding $X\hookrightarrow J$ with respect to a $K$-rational point of $X$. A consequence of the main result of the present paper is that if, moreover, $J$ has good reduction over $W$, then every torsion point on $X$ is {\it $K$-rational} {\it after multiplying $p$}. This result is closely related to a conjecture of {\it R. Coleman} concerning the ramification of torsion points. For instance, this result leads us to a solution of the conjecture in the case where a given curve is hyperelliptic and of genus at least $p$.
</p>projecteuclid.org/euclid.ojm/1508486579_20171020040335Fri, 20 Oct 2017 04:03 EDTPerturbation of irregular Weyl-Heisenberg wave packet frames in $L^2(\mathbb{R})$https://projecteuclid.org/euclid.ojm/1508486580<strong>Raj Kumar</strong>, <strong>Ashok K. SAH</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 791--801.</p><p><strong>Abstract:</strong><br/>
In this paper, we consider the perturbation problem of irregular Weyl-Heisenberg wave packet frame $\{D_{a_j}T_{bk}E_{c_m}\psi\}_{j,k,m\in \mathbb{Z}}$ about dilation, translation and modulation parameters. We give a method to determine whether the perturbation systems is a frame for wave packet functions whose Fourier transforms have small support and prove the stability about dilation parameter on Paley-Wiener space. For a wave packet function, we give a definite answer to the stability about translation parameter $b$.
</p>projecteuclid.org/euclid.ojm/1508486580_20171020040335Fri, 20 Oct 2017 04:03 EDTRealizing homology classes up to cobordismhttps://projecteuclid.org/euclid.ojm/1508486581<strong>Mark Grant</strong>, <strong>András SZŰCS</strong>, <strong>Tamás Terpai</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 803--807.</p><p><strong>Abstract:</strong><br/>
It is known that neither immersions nor maps with a fixed finite set of multisingularities are enough to realize all mod $2$ homology classes in manifolds. In this paper we define the notion of realizing a homology class up to cobordism; it is shown that for realization in this weaker sense immersions are sufficient, but maps with a fixed finite set of multisingularities are still insufficient.
</p>projecteuclid.org/euclid.ojm/1508486581_20171020040335Fri, 20 Oct 2017 04:03 EDTGroups of automorphisms of bordered orientable Klein surfaces of topological genus 2https://projecteuclid.org/euclid.ojm/1508486582<strong>E. Bujalance</strong>, <strong>J.J. Etayo</strong>, <strong>E. Martínez</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 54, Number 4, 809--824.</p><p><strong>Abstract:</strong><br/>
In this paper, we obtain the groups of automorphisms of orientable bordered Klein surfaces of topological genus $2$. For each of those groups $G$ we determine the values of $k$ such that $G$ acts on a surface with $k$ boundary components. Besides, for each given $k$ we exhibit the groups acting on a surface with $k$ boundary components.
</p>projecteuclid.org/euclid.ojm/1508486582_20171020040335Fri, 20 Oct 2017 04:03 EDTThe arc metric on Teichmüller spaces of surfaces of infinite type with boundaryhttps://projecteuclid.org/euclid.ojm/1515661214<strong>Qiyu Chen</strong>, <strong>Lixin Liu</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 1, 1--38.</p><p><strong>Abstract:</strong><br/>
Let $X_{0}$ be a complete hyperbolic surface of infinite type with geodesic boundary which admits a countable pair of pants decomposition. As an application of the Basmajian identity for complete bordered hyperbolic surfaces of infinite type with limit sets of 1-dimensional measure zero, we define an asymmetric metric (which is called arc metric) on the quasiconformal Teichmüller space $\mathcal{T}(X_{0})$ provided that $X_{0}$ satisfies a geometric condition. Furthermore, we construct several examples of hyperbolic surfaces of infinite type satisfying the geometric condition and discuss the relation between the Shiga's condition and the geometric condition.
</p>projecteuclid.org/euclid.ojm/1515661214_20180111040034Thu, 11 Jan 2018 04:00 ESTOn five dimensional Sasakian Lie algebras with trivial centerhttps://projecteuclid.org/euclid.ojm/1515661215<strong>E. Loiudice</strong>, <strong>A. Lotta</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 1, 39--49.</p><p><strong>Abstract:</strong><br/>
We show that every five-dimensional Sasakian Lie algebra with trivial center is $\varphi$-symmetric. Moreover starting from a particular Sasakian structure on the Lie group $SL(2,\mathbb{R})\times\text{Aff}(\mathbb{R})$ we obtain a family of contact metric $(k,\mu)$ structures whose Boeckx invariants assume all values less than $-1$.
</p>projecteuclid.org/euclid.ojm/1515661215_20180111040034Thu, 11 Jan 2018 04:00 ESTGlobal existence of solutions to an $n$-dimensional parabolic-parabolic system for chemotaxis with logistic-type growth and superlinear productionhttps://projecteuclid.org/euclid.ojm/1515661216<strong>Etsushi Nakaguchi</strong>, <strong>Koichi Osaki</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 1, 51--70.</p><p><strong>Abstract:</strong><br/>
We study the global existence of solutions to an $n$-dimensional parabolic-parabolic system for chemotaxis with logistic-type growth. We introduce superlinear production of a chemoattractant. We then show the global existence of solutions in $L_p$ space $( p > n )$ under certain relations between the degradation and production orders.
</p>projecteuclid.org/euclid.ojm/1515661216_20180111040034Thu, 11 Jan 2018 04:00 ESTRepresentations of quantized coordinate algebras via PBW-type elementshttps://projecteuclid.org/euclid.ojm/1515661217<strong>Hironori Oya</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 1, 71--115.</p><p><strong>Abstract:</strong><br/>
Inspired by the work of Kuniba-Okado-Yamada, we study some tensor product representations of quantized coordinate algebras of symmetrizable Kac-Moody Lie algebras in terms of quantized enveloping algebras. As a consequence, we describe structures and properties of certain reducible representations of quantized coordinate algebras. This paper includes alternative proofs of Soibelman's tensor product theorem and Kuniba-Okado-Yamada's common structure theorem based on our direct calculation method using global bases.
</p>projecteuclid.org/euclid.ojm/1515661217_20180111040034Thu, 11 Jan 2018 04:00 ESTAsymptotic behavior of the solutions for the Laplace equation with a large spectral parameter and the inhomogeneous Robin type conditionshttps://projecteuclid.org/euclid.ojm/1515661218<strong>Masaru Ikehata*</strong>, <strong>Mishio Kawashita**</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 1, 117--163.</p><p><strong>Abstract:</strong><br/>
Reduced problems are elliptic problems with a large parameter (as the spectral parameter) given by the Laplace transform of time dependent problems. In this paper, asymptotic behavior of the solutions of the reduced problem for the classical heat equation in bounded domains with the inhomogeneous Robin type conditions is discussed. The boundary of the domain consists of two disjoint surfaces, outside one and inside one. When there are inhomogeneous Robin type data at both boundaries, it is shown that asymptotics of the value of the solution with respect to the large parameter at a given point inside the domain is closely connected to the distance from the point to the both boundaries. It is also shown that if the inside boundary is strictly convex and the data therein vanish, then the asymptotics is different from the previous one. The method for the proof employs a representation of the solution via single layer potentials. It is based on some non trivial estimates on the integral kernels of related integral equations which are previously established and used in studying an inverse problem for the heat equation via the enclosure method.
</p>projecteuclid.org/euclid.ojm/1515661218_20180111040034Thu, 11 Jan 2018 04:00 ESTA rigidity of equivariant holomorphic maps into a complex Grassmannian induced from orthogonal direct sums of holomorphic line bundleshttps://projecteuclid.org/euclid.ojm/1515661219<strong>Isami Koga</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 1, 165--176.</p><p><strong>Abstract:</strong><br/>
In the present paper, we study holomorphic maps induced from orthogonal direct sums of holomorphic line bundles over a compact simply connected homogeneous Kähler manifold into a complex Grassmannian. Then we show if such maps are equivariant, then they are unique up to complex isometry.
</p>projecteuclid.org/euclid.ojm/1515661219_20180111040034Thu, 11 Jan 2018 04:00 EST$\delta$-homogeneity in Finsler geometry and the positive curvature problemhttps://projecteuclid.org/euclid.ojm/1515661220<strong>Ming Xu</strong>, <strong>Lei Zhang*</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 1, 177--194.</p><p><strong>Abstract:</strong><br/>
In this paper, we explore the similarity between normal homogeneity and $\delta$-homogeneity in Finsler geometry. They are both non-negatively curved Finsler spaces. We show that any connected $\delta$-homogeneous Finsler space is $G$-$\delta$-homogeneous, for some suitably chosen connected quasi-compact $G$. So $\delta$-homogeneous Finsler metrics can be defined by a bi-invariant singular metric on $G$ and submersion, just as normal homogeneous metrics, using a bi-invariant Finsler metric on $G$ instead. More careful analysis shows, in the space of all Finsler metrics on $G/H$, the subset of all $G$-$\delta$-homogeneous ones is in fact the closure for the subset of all $G$-normal ones, in the local $C^0$-topology (Theorem 1.1). Using this approximation technique, the classification work for positively curved normal homogeneous Finsler spaces can be applied to classify positively curved $\delta$-homogeneous Finsler spaces, which provides the same classification list. As a by-product, this argument tells more about $\delta$-homogeneous Finsler metrics satisfying the (FP) condition (a weaker version of positively curved condition).
</p>projecteuclid.org/euclid.ojm/1515661220_20180111040034Thu, 11 Jan 2018 04:00 ESTÉtale endomorphisms of 3-folds. Ihttps://projecteuclid.org/euclid.ojm/1524038727<strong>Yoshio Fujimoto</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 2, 195--257.</p><p><strong>Abstract:</strong><br/>
This paper is the first part of our project towards classifications of smooth projective $3$-folds $X$ with $\kappa(X) = -\infty$ admitting a non-isomorphic étale endomorphism. We can prove that for any extremal ray $R$ of divisorial type, the contraction morphism $\pi_R\colon X\to X'$ associated to $R$ is the blowing-up of a smooth $3$-fold $X'$ along an elliptic curve. The difficulty is that there may exist infinitely many extremal rays on $X$. Thus we introduce the notion of an `ESP' which is an infinite sequence of non-isomorphic finite étale coverings of $3$-folds with constant Picard number. We can run the minimal model program (`MMP') with respect to an ESP and obtain the `FESP' $Y_{\bullet}$ of $(X, f)$ which is a distinguished ESP with \textit{extremal rays of fiber type} (cf. Definition 3.6). We first classify $Y_{\bullet}$ and then blow-up $Y_{\bullet}$ along elliptic curves to recover the original $X$. The finiteness of extremal rays of $\overline{\rm NE}(X)$ is verified in certain cases (cf. Theorem 1.4). We encounter a new phenomenon showing that our \'{e}taleness assumption is related with torsion line bundles on an elliptic curve (cf. Theorem 1.5).
</p>projecteuclid.org/euclid.ojm/1524038727_20180418040536Wed, 18 Apr 2018 04:05 EDTGalois covers of type $(p,\cdots,p)$, vanishing cycles formula, and the existence of torsor structureshttps://projecteuclid.org/euclid.ojm/1524038728<strong>Mohamed Saïdi</strong>, <strong>Nicholas Williams</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 2, 259--296.</p><p><strong>Abstract:</strong><br/>
In this article we prove a local Riemman-Hurwitz formula which compares the dimensions of the spaces of vanishing cycles in a finite Galois cover of type $(p,p,\cdots,p)$ between formal germs of $p$-adic curves and which generalises the formula proven in [6] in the case of Galois covers of degree $p$. We also investigate the problem of the existence of a torsor structure for a finite Galois cover of type $(p,p,\cdots,p)$ between $p$-adic schemes.
</p>projecteuclid.org/euclid.ojm/1524038728_20180418040536Wed, 18 Apr 2018 04:05 EDTOn calculations of the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-linkshttps://projecteuclid.org/euclid.ojm/1524038729<strong>Atsushi Ishii</strong>, <strong>Ryo Nikkuni</strong>, <strong>Kanako Oshiro</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 2, 297--313.</p><p><strong>Abstract:</strong><br/>
There are many studies about twisted Alexander invariants for knots and links, but calculations of twisted Alexander invariants for spatial graphs, handlebody-knots, and surface-links have not been demonstrated well. In this paper, we give some remarks to calculate the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-links, and observe their behaviors. For spatial graphs, we calculate the invariants of Suzuki's theta-curves and show that the invariants are nontrivial for Suzuki's theta-curves whose Alexander ideals are trivial. For handlebody-knots, we give a remark on abelianizations and calculate the invariant of the handlebody-knots up to six crossings. For surface-links, we correct Yoshikawa's table and calculate the invariants of the surface-links in the table.
</p>projecteuclid.org/euclid.ojm/1524038729_20180418040536Wed, 18 Apr 2018 04:05 EDTOn the digital representation of integers with bounded prime factorshttps://projecteuclid.org/euclid.ojm/1524038730<strong>Yann Bugeaud</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 2, 315--324.</p><p><strong>Abstract:</strong><br/>
Let $b \ge 2$ be an integer. Not much is known on the representation in base $b$ of prime numbers or of numbers whose prime factors belong to a given, finite set. Among other results, we establish that any sufficiently large integer which is not a multiple of $b$ and has only small (in a suitable sense) prime factors has at least four nonzero digits in its representation in base $b$.
</p>projecteuclid.org/euclid.ojm/1524038730_20180418040536Wed, 18 Apr 2018 04:05 EDTBiharmonic submanifolds in a Riemannian manifoldhttps://projecteuclid.org/euclid.ojm/1524038731<strong>Norihito Koiso</strong>, <strong>Hajime Urakawa</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 2, 325--346.</p><p><strong>Abstract:</strong><br/>
In this paper, we solve affirmatively B.-Y. Chen's conjecture for hypersurfaces in the Euclidean space, under a generic condition. More precisely, every biharmonic hypersurface of the Euclidean space must be minimal if their principal curvatures are simple, and the associated frame field is irreducible.
</p>projecteuclid.org/euclid.ojm/1524038731_20180418040536Wed, 18 Apr 2018 04:05 EDTComparison theorems in pseudo-Hermitian geometry and applicationshttps://projecteuclid.org/euclid.ojm/1524038732<strong>Yuxin Dong</strong>, <strong>Wei Zhang</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 2, 347--367.</p><p><strong>Abstract:</strong><br/>
In this paper, we study the theory of geodesics with respect to the Tanaka-Webster connection in a pseudo-Hermitian manifold, aiming to generalize some comparison results in Riemannian geometry to the case of pseudo-Hermitian geometry. Some Hopf-Rinow type, Cartan-Hadamard type and Bonnet-Myers type results are established.
</p>projecteuclid.org/euclid.ojm/1524038732_20180418040536Wed, 18 Apr 2018 04:05 EDTType numbers of quaternion hermitian forms and supersingular abelian varietieshttps://projecteuclid.org/euclid.ojm/1524038733<strong>Tomoyoshi Ibukiyama</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 2, 369--384.</p><p><strong>Abstract:</strong><br/>
The word \textit{type number} of an algebra means classically the number of isomorphism classes of maximal orders in the algebra, but here we consider quaternion hermitian lattices in a fixed genus and their right orders. Instead of inner isomorphism classes of right orders, we consider isomorphism classes realized by similitudes of the quaternion hermitian forms.The number $T$ of such isomorphism classes are called \textit{type number} or \textit{$G$-type number}, where $G$ is the group of quaternion hermitian similitudes. We express $T$ in terms of traces of some special Hecke operators. This is a generalization of the result announced in [5] (I) from the principal genus to general lattices. We also apply our result to the number of isomorphism classes of any polarized superspecial abelian varieties which have a model over ${\Bbb F}_p$ such that the polarizations are in a "fixed genus of lattices". This is a generalization of [8] and has an application to the number of components in the supersingular locus which are defined over ${\Bbb F}_p$.
</p>projecteuclid.org/euclid.ojm/1524038733_20180418040536Wed, 18 Apr 2018 04:05 EDTA remark on conditions that a diffusion in the natural scale is a martingalehttps://projecteuclid.org/euclid.ojm/1524038734<strong>Yuuki Shimizu</strong>, <strong>Fumihiko Nakano</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 2, 385--391.</p><p><strong>Abstract:</strong><br/>
We consider a diffusion processes $\{ X_t \}$ on an interval in the natural scale. Some results are known under which $\{ X_t \}$ is a martingale, and we give simple and analytic proofs for them.
</p>projecteuclid.org/euclid.ojm/1524038734_20180418040536Wed, 18 Apr 2018 04:05 EDTOn the flat geometry of the cuspidal edgehttps://projecteuclid.org/euclid.ojm/1530691235<strong>Raúl Oset Sinha</strong>, <strong>Farid Tari</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 393--421.</p><p><strong>Abstract:</strong><br/>
We study the geometry of the cuspidal edge $M$ in $\mathbb{R}^3$ derived from its contact with planes and lines (referred to as flat geometry). The contact of $M$ with planes is measured by the singularities of the height functions on $M$. We classify submersions on a model of $M$ by diffeomorphisms and recover the contact of $M$ with planes from that classification. The contact of $M$ with lines is measured by the singularities of orthogonal projections of $M$. We list the generic singularities of the projections and obtain the generic deformations of the apparent contour (profile) when the direction of projection varies locally in $S^2$. We also relate the singularities of the height functions and of the projections to some geometric invariants of the cuspidal edge.
</p>projecteuclid.org/euclid.ojm/1530691235_20180704040042Wed, 04 Jul 2018 04:00 EDTBloch's conjecture for Enriques varietieshttps://projecteuclid.org/euclid.ojm/1530691236<strong>Robert Laterveer</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 423--438.</p><p><strong>Abstract:</strong><br/>
Enriques varieties have been defined as higher-dimensional generalizations of Enriques surfaces. Bloch's conjecture implies that Enriques varieties should have trivial Chow group of zero-cycles. We prove this is the case for all known examples of irreducible Enriques varieties of index larger than $2$. The proof is based on results concerning the Chow motive of generalized Kummer varieties.
</p>projecteuclid.org/euclid.ojm/1530691236_20180704040042Wed, 04 Jul 2018 04:00 EDTRank-one Perturbation of Weighted Shifts on a Directed Tree: Partial Normality and Weak Hyponormalityhttps://projecteuclid.org/euclid.ojm/1530691237<strong>George R. Exner</strong>, <strong>Il Bong Jung</strong>, <strong>Eun Young Lee</strong>, <strong>Minjung Seo</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 439--462.</p><p><strong>Abstract:</strong><br/>
A special rank-one perturbation $S_{t,n}$ of a weighted shift on a directed tree is constructed. Partial normality and weak hyponormality (including quasinormality, $p$-hyponormality, $p$-paranormality, absolute-$p$-paranormality and $A(p)$-class) of $S_{t,n}$ are characterized.
</p>projecteuclid.org/euclid.ojm/1530691237_20180704040042Wed, 04 Jul 2018 04:00 EDTOn-diagonal Heat Kernel Lower Bound for Strongly Local Symmetric Dirichlet Formshttps://projecteuclid.org/euclid.ojm/1530691238<strong>Shuwen Lou</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 463--477.</p><p><strong>Abstract:</strong><br/>
This paper studies strongly local symmetric Dirichlet forms on general measure spaces. The underlying space is equipped with the intrinsic metric induced by the Dirichlet form, with respect to which the metric measure space does not necessarily satisfy volume-doubling property. Assuming Nash-type inequality, it is proved in this paper that outside a properly exceptional set, if a pointwise on-diagonal heat kernel upper bound in terms of the volume function is known a priori, then the comparable heat kernel lower bound also holds. The only assumption made on the volume growth rate is that it can be bounded by a continuous function satisfying doubling property, in other words, is not exponential.
</p>projecteuclid.org/euclid.ojm/1530691238_20180704040042Wed, 04 Jul 2018 04:00 EDTMazur manifolds and corks with small shadow complexitieshttps://projecteuclid.org/euclid.ojm/1530691239<strong>Hironobu Naoe</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 479--498.</p><p><strong>Abstract:</strong><br/>
In this paper we show that there exist infinitely many Mazur type manifolds and corks with shadow complexity one among the 4-manifolds constructed from contractible special polyhedra having one true vertex by using the notion of Turaev's shadow. We also find such manifolds among 4-manifolds constructed from Bing's house. Our manifolds with shadow complexity one contain the Mazur manifolds $W^{\pm }(l,k)$ which were studied by Akbulut and Kirby.
</p>projecteuclid.org/euclid.ojm/1530691239_20180704040042Wed, 04 Jul 2018 04:00 EDTOn Kohnen plus-space of Jacobi forms of half integral weight of matrix indexhttps://projecteuclid.org/euclid.ojm/1530691240<strong>Shuichi Hayashida</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 499--522.</p><p><strong>Abstract:</strong><br/>
We introduce a plus-space of Jacobi forms, which is a certain subspace of Jacobi forms of half-integral weight of matrix index. This is an analogue to the Kohnen plus-space in the framework of Jacobi forms. We shall show a linear isomorphism between the plus-space of Jacobi forms and the space of Jacobi forms of integral weight of certain matrix index. Moreover, we shall show that this linear isomorphism is compatible with the action of Hecke operators of both spaces. This result is a kind of generalization of Eichler-Zagier-Ibukiyama correspondence, which is an isomorphism between the generalized plus-space of Siegel modular forms of general degree and Jacobi forms of index $1$ of general degree.
</p>projecteuclid.org/euclid.ojm/1530691240_20180704040042Wed, 04 Jul 2018 04:00 EDTAnswer to a Question by Nakamura, Nakanishi, and Satoh involving crossing numbers of knotshttps://projecteuclid.org/euclid.ojm/1530691241<strong>Jun Ge</strong>, <strong>Xian'an Jin</strong>, <strong>Louis H. Kauffman</strong>, <strong>Pedro Lopes</strong>, <strong>Lianzhu Zhang</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 523--527.</p><p><strong>Abstract:</strong><br/>
In this paper we give a positive answer to a question raised by Nakamura, Nakanishi, and Satoh concerning an inequality involving crossing numbers of knots. We show it is an equality only for the trefoil and for the figure-eight knots.
</p>projecteuclid.org/euclid.ojm/1530691241_20180704040042Wed, 04 Jul 2018 04:00 EDT$L^2$-Burau maps and $L^2$-Alexander torsionshttps://projecteuclid.org/euclid.ojm/1530691242<strong>Fathi Ben Aribi</strong>, <strong>Anthony Conway</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 529--545.</p><p><strong>Abstract:</strong><br/>
It is well known that the Burau representation of the braid group can be used to recover the Alexander polynomial of the closure of a braid. We define $L^2$-Burau maps and use them to compute some $L^2$-Alexander torsions of links. As an application, we prove that the $L^2$-Burau maps distinguish more braids than the Burau representation.
</p>projecteuclid.org/euclid.ojm/1530691242_20180704040042Wed, 04 Jul 2018 04:00 EDTInitial-boundary value problem for the degenerate hyperbolic equation of a hanging stringhttps://projecteuclid.org/euclid.ojm/1530691243<strong>Masahiro Takayama</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 547--565.</p><p><strong>Abstract:</strong><br/>
We consider an initial-boundary value problem for the degenerate linear hyperbolic equation as a model of the motion of an inextensible string fixed at one end in the gravity field. We shall show the existence and the uniqueness of the solution and study the regularity of the solution.
</p>projecteuclid.org/euclid.ojm/1530691243_20180704040042Wed, 04 Jul 2018 04:00 EDTA complete description of the antipodal set of most symmetric spaces of compact typehttps://projecteuclid.org/euclid.ojm/1530691244<strong>Jonas Beyrer</strong>. <p><strong>Source: </strong>Osaka Journal of Mathematics, Volume 55, Number 3, 567--586.</p><p><strong>Abstract:</strong><br/>
It is known that the antipodal set of a Riemannian symmetric space of compact type $G/K$ consists of a union of $K$-orbits. We determine the dimensions of these $K$-orbits of most irreducible symmetric spaces of compact type. The symmetric spaces we are not going to deal with are those with restricted root system $\mathfrak{a}_r$ and a non-trivial fundamental group, which is not isomorphic to $\mathbb{Z}_2$ or $\mathbb{Z}_{r+1}$. For example, we show that the antipodal sets of the Lie groups $Spin(2r+1)\:\: r\geq 5$, $E_8$ and $G_2$ consist only of one orbit which is of dimension $2r$, 128 and 6, respectively; $SO(2r+1)$ has also an antipodal set of dimension $2r$; and the Grassmannian $Gr_{r,r+q}(\mathbb{R})$ has a $rq$-dimensional orbit as antipodal set if $r\geq 5$ and $r\neq q>0$.
</p>projecteuclid.org/euclid.ojm/1530691244_20180704040042Wed, 04 Jul 2018 04:00 EDT