Kodai Mathematical Journal Articles (Project Euclid)
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The latest articles from Kodai Mathematical Journal 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 EDTThu, 31 Mar 2011 09:07 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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Remarks on complete non-compact gradient Ricci expanding solitons
http://projecteuclid.org/euclid.kmj/1278076334
<strong>Li Ma</strong>, <strong>Dezhong Chen</strong><p><strong>Source: </strong>Kodai Math. J., Volume 33, Number 2, 173--181.</p><p><strong>Abstract:</strong><br/> In this paper, we study gradient Ricci expanding solitons ( X,g ) satisfying Rc = cg + D 2 f , where Rc is the Ricci curvature, c < 0 is a constant, and D 2 f is the Hessian of the potential function f on X . We show that for a gradient expanding soliton ( X,g ) with non-negative Ricci curvature, the scalar curvature R has at most one maximum point on X , which is the only minimum point of the potential function f . Furthermore, R > 0 on X unless ( X,g ) is Ricci flat. We also show that there is exponentially decay for scalar curvature on a complete non-compact expanding soliton with its Ricci curvature being ε-pinched. </p>projecteuclid.org/euclid.kmj/1278076334_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTAlmost automorphic solutions of semilinear stochastic hyperbolic differential equations in intermediate spacehttps://projecteuclid.org/euclid.kmj/1509415229<strong>Zhinan Xia</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 492--517.</p><p><strong>Abstract:</strong><br/>
In this paper, we investigate the existence, uniqueness of almost automorphic in one-dimensional distribution mild solution for semilinear stochastic differential equations driven by Lévy noise. The semigroup theory, fixed point theorem and stochastic analysis technique are the main tools in carrying out proof. Finally, we give one example to illustrate the main findings.
</p>projecteuclid.org/euclid.kmj/1509415229_20171030220055Mon, 30 Oct 2017 22:00 EDTL p p -harmonic 1-forms on locally conformally flat Riemannian manifoldshttps://projecteuclid.org/euclid.kmj/1509415230<strong>Yingbo Han</strong>, <strong>Qianyu Zhang</strong>, <strong>Mingheng Liang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 518--536.</p><p><strong>Abstract:</strong><br/>
In this paper, we obtain some vanishing and finiteness theorems for L p p -harmonic 1-forms on a locally conformally flat Riemmannian manifolds which satisfies an integral pinching condition on the traceless Ricci tensor, and for which the scalar curvature satisfies pinching curvature conditions or the first eigenvalue of the Laplace-Beltrami operator of M is bounded by a suitable constant.
</p>projecteuclid.org/euclid.kmj/1509415230_20171030220055Mon, 30 Oct 2017 22:00 EDTNote on restriction maps of Chow rings to Weyl group invariantshttps://projecteuclid.org/euclid.kmj/1509415231<strong>Nobuaki Yagita</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 537--552.</p><p><strong>Abstract:</strong><br/>
Let G be an algebraic group over C corresponding a compact simply connected Lie group. When H *( G ) has p -torsion, we see ρ* CH : CH *( BG ) → CH *( BT ) W G ( T ) is always not surjective. We also study the algebraic cobordism version ρ* Ω . In particular when G = Spin (7) and p = 2, we see each Griffiths element in CH *( BG ) is detected by an element in Ω*( BT ).
</p>projecteuclid.org/euclid.kmj/1509415231_20171030220055Mon, 30 Oct 2017 22:00 EDTOn infinitesimal Strebel pointshttps://projecteuclid.org/euclid.kmj/1509415232<strong>Alastair Fletcher</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 553--561.</p><p><strong>Abstract:</strong><br/>
In this paper, we prove that if X is a Riemann surface of infinite analytic type and [μ] T is any element of Teichmüller space, then there exists μ 1 $\in$ [μ] T so that [μ 1 ] B is an infinitesimal Strebel point.
</p>projecteuclid.org/euclid.kmj/1509415232_20171030220055Mon, 30 Oct 2017 22:00 EDTGround state solutions for asymptotically periodic linearly coupled Schrödinger equations with critical exponenthttps://projecteuclid.org/euclid.kmj/1509415233<strong>Sitong Chen</strong>, <strong>XianHua Tang</strong>, <strong>Jianxiong Li</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 562--576.</p><p><strong>Abstract:</strong><br/>
We consider the following system of coupled nonlinear Schrödinger equations
$$\left\{\begin{array}{ll}-\triangle u+a(x) u=|u|^{p-2}u+\lambda(x) v, x\in \mathbb{R}^N,\\-\triangle v+b(x) v=|v|^{2^*-2}v+\lambda(x) u, x\in \mathbb{R}^N,\\u,v\in H^1(\mathbb{R}^N), \end{array}\right.$$
where N ≥ 3, 2 < p < 2*, 2* = 2 N /( N −2) is the Sobolev critical exponent, a , b , λ $\in$ C ( R N , R ) $\cap$ L ∞ ( R N , R ) and a ( x ), b ( x ) and λ( x ) are asymptotically periodic, and can be sign-changing. By using a new technique, we prove the existence of a ground state of Nehari type solution for the above system under some mild assumptions on a , b and λ. In particular, the common condition that |λ( x )| < $\sqrt{a(x)b(x)}$ for all x $\in$ R N is not required.
</p>projecteuclid.org/euclid.kmj/1509415233_20171030220055Mon, 30 Oct 2017 22:00 EDTA note on Atiyah's Γ-index theorem in Heisenberg calculushttps://projecteuclid.org/euclid.kmj/1509415234<strong>Tatsuki Seto</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 577--583.</p><p><strong>Abstract:</strong><br/>
In this note, we prove an index theorem on Galois coverings for Heisenberg elliptic (but not elliptic) differential operators, which is analogous to Atiyah's Γ-index theorem. This note also contains an example of Heisenberg differential operators with non-trivial Γ-index.
</p>projecteuclid.org/euclid.kmj/1509415234_20171030220055Mon, 30 Oct 2017 22:00 EDTAbsolute zeta functions and the automorphyhttps://projecteuclid.org/euclid.kmj/1509415235<strong>Nobushige Kurokawa</strong>, <strong>Hidekazu Tanaka</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 584--614.</p><p><strong>Abstract:</strong><br/>
</p>projecteuclid.org/euclid.kmj/1509415235_20171030220055Mon, 30 Oct 2017 22:00 EDTOn endomorphisms of hypersurfaceshttps://projecteuclid.org/euclid.kmj/1509415236<strong>Ilya Karzhemanov</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 615--624.</p><p><strong>Abstract:</strong><br/>
For any prime p ≥ 5, we show that generic hypersurface X p $subset$ P p defined over Q admits a non-trivial rational dominant self-map of degree > 1, defined over $\overline{\mathbb{Q}}$ . A simple arithmetic application of this fact is also given.
</p>projecteuclid.org/euclid.kmj/1509415236_20171030220055Mon, 30 Oct 2017 22:00 EDTThe Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus onehttps://projecteuclid.org/euclid.kmj/1509415237<strong>Yuichiro Hoshi</strong>, <strong>Ryo Kinoshita</strong>, <strong>Chikara Nakayama</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 625--637.</p><p><strong>Abstract:</strong><br/>
We study the Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus one. A consequence of the main results is that the isomorphism class of a certain moduli space of hyperbolic curves of genus one over a sub- p -adic field is completely determined by the isomorphism class of the étale fundamental group of the moduli space over the absolute Galois group of the sub- p -adic field. We also prove related results in absolute anabelian geometry.
</p>projecteuclid.org/euclid.kmj/1509415237_20171030220055Mon, 30 Oct 2017 22:00 EDTClassification results of quasi Einstein solitonshttps://projecteuclid.org/euclid.kmj/1509415238<strong>Shu Yau Huang</strong>, <strong>Lin Feng Wang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 638--647.</p><p><strong>Abstract:</strong><br/>
We classify (ρ,τ)-quasi Einstein solitons with ( a ,τ)-concurrent vector fields. We also give a necessary and sufficient condition for a submanifold to be a (ρ,τ)-quasi Einstein soliton in a Riemannian manifold equipped with an ( a ,τ)-concurrent vector field.
</p>projecteuclid.org/euclid.kmj/1509415238_20171030220055Mon, 30 Oct 2017 22:00 EDTVanishing of Killing vector fields on compact Finsler manifoldshttps://projecteuclid.org/euclid.kmj/1521424815<strong>Bin Shen</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 1--15.</p><p><strong>Abstract:</strong><br/>
In this paper, we define a new Ricci curvature on Finsler manifold named the mean Ricci curvature, which is useful in the study of different symmetric fields on manifolds. By presenting a Bochner type formula of Killing vector fields on general Finsler manifolds, we prove the vanishing theorem of the Killing vector fields on any compact Finsler manifold with a negative mean Ricci curvature. This result involves the vanishing theorem of Killing vector fields in the Riemannian case.
</p>projecteuclid.org/euclid.kmj/1521424815_20180320003217Tue, 20 Mar 2018 00:32 EDTDehn twists on Kauffman bracket skein algebrashttps://projecteuclid.org/euclid.kmj/1521424819<strong>Shunsuke Tsuji</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 16--41.</p><p><strong>Abstract:</strong><br/>
We give an explicit formula for the action of the Dehn twist along a simple closed curve in a compact connected oriented surface on the completion of the filtered skein modules of the surface. To do this, we introduce filtrations of the Kauffman bracket skein algebra and the Kauffman bracket skein modules of the surface.
</p>projecteuclid.org/euclid.kmj/1521424819_20180320003217Tue, 20 Mar 2018 00:32 EDTOn 3-dimensional homogeneous generalized $m$-quasi-Einstein manifoldshttps://projecteuclid.org/euclid.kmj/1521424822<strong>Zejun Hu</strong>, <strong>Dehe Li</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 42--51.</p><p><strong>Abstract:</strong><br/>
In this paper, we show that for 3-dimensional homogeneous manifolds only the space form can carry a proper generalized $m$-quasi-Einstein structure.
</p>projecteuclid.org/euclid.kmj/1521424822_20180320003217Tue, 20 Mar 2018 00:32 EDTAn effective Schmidt's subspace theorem for hypersurfaces in subgeneral position in projective varieties over function fieldshttps://projecteuclid.org/euclid.kmj/1521424823<strong>Giang Le</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 52--69.</p><p><strong>Abstract:</strong><br/>
We established an effective version of Schmidt's subspace theorem on a smooth projective variety $\mathcal{X}$ over function fields of characteristic zero for hypersurfaces located in $m$-subgeneral position with respect to $\mathcal{X}$.
</p>projecteuclid.org/euclid.kmj/1521424823_20180320003217Tue, 20 Mar 2018 00:32 EDTAn isoperimetric inequality for diffused surfaceshttps://projecteuclid.org/euclid.kmj/1521424824<strong>Ulrich Menne</strong>, <strong>Christian Scharrer</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 70--85.</p><p><strong>Abstract:</strong><br/>
For general varifolds in Euclidean space, we prove an isoperimetric inequality, adapt the basic theory of generalised weakly differentiable functions, and obtain several Sobolev type inequalities. We thereby intend to facilitate the use of varifold theory in the study of diffused surfaces.
</p>projecteuclid.org/euclid.kmj/1521424824_20180320003217Tue, 20 Mar 2018 00:32 EDTTwisted Alexander polynomials of genus one two-bridge knotshttps://projecteuclid.org/euclid.kmj/1521424825<strong>Anh T. Tran</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 86--97.</p><p><strong>Abstract:</strong><br/>
Morifuji [14] computed the twisted Alexander polynomial of twist knots for nonabelian representations. In this paper we compute the twisted Alexander polynomial and Reidemeister torsion of genus one two-bridge knots, a class of knots which includes twist knots. As an application, we give a formula for the Reidemeister torsion of the 3-manifold obtained by $\frac{1}{q}$-Dehn surgery on a genus one two-bridge knot.
</p>projecteuclid.org/euclid.kmj/1521424825_20180320003217Tue, 20 Mar 2018 00:32 EDTLinear Weingarten spacelike hypersurfaces in Lorentz space forms with prescribed Gauss maphttps://projecteuclid.org/euclid.kmj/1521424826<strong>Xiaoli Chao</strong>, <strong>Yusha Lv</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 98--114.</p><p><strong>Abstract:</strong><br/>
This paper address the geometry of complete linear Weingarten spacelike hypersurfaces in the Lorentz space forms. First, a divergence lemma concerning linear Weingarten spacelike hypersurfaces is obtained. Then, with the aid of this lemma, by supposing suitable restrictions on the Gauss map, we show that such hypersurfaces must be totally umbilical, which are some extension of the recent results of Aquino, Bezerra and Lima [7] and Aquino, Lima and Velásquez [11].
</p>projecteuclid.org/euclid.kmj/1521424826_20180320003217Tue, 20 Mar 2018 00:32 EDTUniqueness theorem for meromorphic mappings with multiple valueshttps://projecteuclid.org/euclid.kmj/1521424827<strong>Ha Huong Giang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 115--124.</p><p><strong>Abstract:</strong><br/>
In this article, we will prove a uniqueness theorem for meromorphic mappings into complex projective space $\mathbf{P}^n(\mathbf{C})$ with different multiple values and a general condition on the intersections of the inverse images of these hyperplanes.
</p>projecteuclid.org/euclid.kmj/1521424827_20180320003217Tue, 20 Mar 2018 00:32 EDTDegeneration of period matrices of stable curveshttps://projecteuclid.org/euclid.kmj/1521424828<strong>Yu Yang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 125--153.</p><p><strong>Abstract:</strong><br/>
In the present paper, we study the extent to which linear combinations of period matrices arising from stable curves are degenerate (i.e., as bilinear forms). We give a criterion to determine whether a stable curve admits such a degenerate linear combination of period matrices. In particular, this criterion can be interpreted as a certain analogue of the weight-monodromy conjecture for non-degenerate elements of pro-$\ell$ log étale fundamental groups of certain log points associated to the log stack $\overline{\mathcal{M}}_{g}^{log}$.
</p>projecteuclid.org/euclid.kmj/1521424828_20180320003217Tue, 20 Mar 2018 00:32 EDTGenerators for the mapping class group of a nonorientable surfacehttps://projecteuclid.org/euclid.kmj/1521424829<strong>Susumu Hirose</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 154--159.</p><p><strong>Abstract:</strong><br/>
We show that Szepietowski's system of generators for the mapping class group of a non-orientable surface is a minimal generating set by Dehn twists and $Y$-homemorphisms.
</p>projecteuclid.org/euclid.kmj/1521424829_20180320003217Tue, 20 Mar 2018 00:32 EDTA lower bound for the number of integral solutions of Mordell equationhttps://projecteuclid.org/euclid.kmj/1521424830<strong>Hassan Shabani-Solt</strong>, <strong>Ali S. Janfada</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 160--166.</p><p><strong>Abstract:</strong><br/>
For a nonzero integer $d$, a celebrated Siegel Theorem says that the number $N(d)$ of integral solutions of Mordell equation $y^2+x^3=d$ is finite. We find a lower bound for $N(d)$, showing that the number of solutions of Mordell equation increases dramatically. We also prove that for any positive integer $n$, there is an integer square multiply represented by Mordell equations, i.e., $k^2=y_1^2+x_1^3=y_2^2+x_2^3=\cdots =y_n^2+x_n^3$.
</p>projecteuclid.org/euclid.kmj/1521424830_20180320003217Tue, 20 Mar 2018 00:32 EDTA regulator map for 1-cycles with modulushttps://projecteuclid.org/euclid.kmj/1521424831<strong>Mirai Onoda</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 167--200.</p><p><strong>Abstract:</strong><br/>
Let $k$ be a field of characteristic 0. We define a map from the additive higher Chow group of 1-cycles with strong sup $m$-modulus $CH_1(A_k(m), n)_{ssup}$ to the module of absolute Kähler differentials of $k$ with twisted $k^*$-action $\Omega^{n-2}_k\langle \omega \rangle$ of weight $\omega$. We will call the map a $\emph{regulator map}$, and we show that the regulator map is surjective if $k$ is an algebraically closed field. In case $\omega = m+1$, this map specializes to Park's regulator map. We study a relationship between the cyclic homology and the additive higher Chow group with strong sup modulus by using our regulator map.
</p>projecteuclid.org/euclid.kmj/1521424831_20180320003217Tue, 20 Mar 2018 00:32 EDTOn complex deformations of Kähler-Ricci solitonshttps://projecteuclid.org/euclid.kmj/1521424832<strong>Nefton Pali</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 201--226.</p><p><strong>Abstract:</strong><br/>
We obtain a formal obstruction, i.e. a necessary condition for the existence of polarized complex deformations of Kähler-Ricci solitons. This obstruction is expressed in terms of the harmonic part of the variation of the complex structure.
</p>projecteuclid.org/euclid.kmj/1521424832_20180320003217Tue, 20 Mar 2018 00:32 EDTZeta functions for Kähler graphshttps://projecteuclid.org/euclid.kmj/1530496832<strong>Yaermaimaiti Tuerxunmaimaiti</strong>, <strong>Toshiaki Adachi</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 227--239.</p><p><strong>Abstract:</strong><br/>
To create a discrete analogue of magnetic fields on Riemannian manifolds is a challenging problem. The notion of Kähler graphs introduced by the second author is one of trials of this discretization. In this article we study the asymptotic behavior of the weighted number of prime cycles with respect to their lengths by use of a zeta function.
</p>projecteuclid.org/euclid.kmj/1530496832_20180701220050Sun, 01 Jul 2018 22:00 EDTCyclic coverings of the projective line by Mumford curves in positive characteristichttps://projecteuclid.org/euclid.kmj/1530496835<strong>Ryota Mikami</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 240--263.</p><p><strong>Abstract:</strong><br/>
We study the rigid analytic geometry of cyclic coverings of the projective line. We determine the defining equation of cyclic coverings of degree $p$ of the projective line by Mumford curves over complete discrete valuation fields of positive characteristic $p$. Previously, Bradley studied that of any degree over non-archimedean local fields of characteristic zero.
</p>projecteuclid.org/euclid.kmj/1530496835_20180701220050Sun, 01 Jul 2018 22:00 EDTUltra-discrete equations and tropical counterparts of some complex analysis resultshttps://projecteuclid.org/euclid.kmj/1530496839<strong>Min-Feng Chen</strong>, <strong>Zong-Sheng Gao</strong>, <strong>Ji-Long Zhang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 264--283.</p><p><strong>Abstract:</strong><br/>
A tropical version of Nevanlinna theory describes value distribution of continuous piecewise linear functions of a real variable. In this paper, we present some results on value distribution theory of tropical difference polynomials and uniqueness theory of tropical entire functions. Application to some ultra-discrete equations is also given.
</p>projecteuclid.org/euclid.kmj/1530496839_20180701220050Sun, 01 Jul 2018 22:00 EDTA non-integrated hypersurface defect relation for meromorphic maps over complete Kähler manifolds into projective algebraic varietieshttps://projecteuclid.org/euclid.kmj/1530496842<strong>Wei Chen</strong>, <strong>Qi Han</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 284--300.</p><p><strong>Abstract:</strong><br/>
In this paper, a non-integrated defect relation for meromorphic maps from complete Kähler manifolds $M$ into smooth projective algebraic varieties $V$ intersecting hypersurfaces located in $k$-subgeneral position (see (1.5) below) is proved. The novelty of this result lies in that both the upper bound and the truncation level of our defect relation depend only on $k$, $\dim_{\,\mathbf{C}}(V)$ and the degrees of the hypersurfaces considered; besides, this defect relation recovers Hirotaka Fujimoto [6, Theorem 1.1] when subjected to the same conditions.
</p>projecteuclid.org/euclid.kmj/1530496842_20180701220050Sun, 01 Jul 2018 22:00 EDTThe Hessian of quantized Ding functionals and its asymptotic behaviorhttps://projecteuclid.org/euclid.kmj/1530496843<strong>Ryosuke Takahashi</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 301--314.</p><p><strong>Abstract:</strong><br/>
We compute the Hessian of quantized Ding functionals and give an elementary proof for the convexity of quantized Ding functionals along Bergman geodesics from the view point of projective geometry. We study also the asymptotic behavior of the Hessian using the Berezin-Toeplitz quantization.
</p>projecteuclid.org/euclid.kmj/1530496843_20180701220050Sun, 01 Jul 2018 22:00 EDTCurvature properties of homogeneous real hypersurfaces in nonflat complex space formshttps://projecteuclid.org/euclid.kmj/1530496844<strong>Sadahiro Maeda</strong>, <strong>Hiroshi Tamaru</strong>, <strong>Hiromasa Tanabe</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 315--331.</p><p><strong>Abstract:</strong><br/>
In this paper, we study curvature properties of all homogeneous real hypersurfaces in nonflat complex space forms, and determine their minimalities and the signs of their sectional curvatures completely. These properties reflect the sign of the constant holomorphic sectional curvature $c$ of the ambient space. Among others, for the case of $c$ < 0 there exist homogeneous real hypersurfaces with positive sectional curvature and also ones with negative sectional curvature, whereas for the case of $c$ > 0 there do not exist any homogeneous real hypersurfaces with nonpositive sectional curvature.
</p>projecteuclid.org/euclid.kmj/1530496844_20180701220050Sun, 01 Jul 2018 22:00 EDTOn Perez Del Pozo's lower bound of Weierstrass weighthttps://projecteuclid.org/euclid.kmj/1530496845<strong>Nan Wangyu</strong>, <strong>Masumi Kawasaki</strong>, <strong>Fumio Sakai</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 332--347.</p><p><strong>Abstract:</strong><br/>
Let $V$ be a smooth projective curve over the complex number field with genus $g \geq 2$, and let $\sigma$ be an automorphism on $V$ such that the quotient curve $V/\langle \sigma \rangle$ has genus 0. We write $d$ (resp., $b$) for the order of $\sigma$ (resp., the number of fixed points of $\sigma$). When $d$ and $b$ are fixed, the lower bound of the (Weierstrass) weights of fixed points of $\sigma$ was obtained by Perez del Pozo [7]. We obtain necessary and sufficient conditions for when the lower bound is attained.
</p>projecteuclid.org/euclid.kmj/1530496845_20180701220050Sun, 01 Jul 2018 22:00 EDTConvexity and the Dirichlet problem of translating mean curvature flowshttps://projecteuclid.org/euclid.kmj/1530496846<strong>Li Ma</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 348--358.</p><p><strong>Abstract:</strong><br/>
In this work, we propose a new evolving geometric flow (called translating mean curvature flow) for the translating solitons of hypersurfaces in $R^{n+1}$. We study the basic properties, such as positivity preserving property, of the translating mean curvature flow. The Dirichlet problem for the graphical translating mean curvature flow is studied and the global existence of the flow and the convergence property are also considered.
</p>projecteuclid.org/euclid.kmj/1530496846_20180701220050Sun, 01 Jul 2018 22:00 EDTOn the complex Łojasiewicz inequality with parameterhttps://projecteuclid.org/euclid.kmj/1530496847<strong>Maciej P. Denkowski</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 359--374.</p><p><strong>Abstract:</strong><br/>
We prove a continuity property in the sense of currents of a continuous family of holomorphic functions which allows us to obtain a Łojasiewicz inequality with an effective exponent independent of the parameter.
</p>projecteuclid.org/euclid.kmj/1530496847_20180701220050Sun, 01 Jul 2018 22:00 EDTBased chord diagrams of spherical curveshttps://projecteuclid.org/euclid.kmj/1530496848<strong>Noboru Ito</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 375--396.</p><p><strong>Abstract:</strong><br/>
This paper demonstrates an approach for developing a framework to produce invariants of base-point-free generic spherical curves under some chosen local moves from Reidemeister moves using based chord diagrams. Our invariants not only contain Arnold's classical generic spherical curve invariant but also new invariants.
</p>projecteuclid.org/euclid.kmj/1530496848_20180701220050Sun, 01 Jul 2018 22:00 EDTFoxby equivalences associated to strongly Gorenstein moduleshttps://projecteuclid.org/euclid.kmj/1530496849<strong>Wanru Zhang</strong>, <strong>Zhongkui Liu</strong>, <strong>Xiaoyan Yang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 397--412.</p><p><strong>Abstract:</strong><br/>
In order to establish the Foxby equivalences associated to strongly Gorenstein modules, we introduce the notions of strongly $\mathcal{W}_P$-Gorenstein, $\mathcal{W}_I$-Gorenstein and $\mathcal{W}_F$-Gorenstein modules and discuss some basic properties of these modules. We show that the subcategory of strongly Gorenstein projective left $R$-modules in the left Auslander class and the subcategory of strongly $\mathcal{W}_P$-Gorenstein left $S$-modules are equivalent under Foxby equivalence. The injective and flat case are also studied.
</p>projecteuclid.org/euclid.kmj/1530496849_20180701220050Sun, 01 Jul 2018 22:00 EDTOn Terai's conjecturehttps://projecteuclid.org/euclid.kmj/1530496850<strong>Xin Zhang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 413--420.</p><p><strong>Abstract:</strong><br/>
Let $p$ be an odd prime such that $b^r+1=2p^t$, where $r$, $t$ are positive integers and $b \equiv$ 3,5 (mod 8). We show that the Diophantine equation $x^2+b^m=p^n$ has only the positive integer solution $(x,m,n)=(p^t-1,r,2t)$. We also prove that if $b$ is a prime and $r=t=2$, then the above equation has only one solution for the case $b \equiv$ 3,5,7 (mod 8) and the case $d$ is not an odd integer greater than 1 if $b \equiv$ 1 (mod 8), where $d$ is the order of prime divisor of ideal ($p$) in the ideal class group of $\mathbf{Q}$ ($\sqrt {-q}$).
</p>projecteuclid.org/euclid.kmj/1530496850_20180701220050Sun, 01 Jul 2018 22:00 EDTThe effect of Fenchel-Nielsen coordinates under elementary moveshttps://projecteuclid.org/euclid.kmj/1530496851<strong>Dong Tan</strong>, <strong>Peijia Liu</strong>, <strong>Xuewen Liu</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 421--439.</p><p><strong>Abstract:</strong><br/>
We describe the effect of Fenchel-Nielsen coordinates under elementary move for hyperbolic surfaces with geodesic boundaries, punctures and cone points, which generalize Okai's result for surfaces with geodesic boundaries. The proof relies on the parametrization of the Teichmüller space of surface of type (1,1) or (0,4) as a sub-locus of an algebraic equation in $\mathbf{R}^3$. As an application, we show that the hyperbolic length functions of closed curves are asymptotically piecewise linear functions with respect to the Fenchel Nielsen coordinates in the Teichmüller spaces of surfaces with cone points.
</p>projecteuclid.org/euclid.kmj/1530496851_20180701220050Sun, 01 Jul 2018 22:00 EDTA prime geodesic theorem for higher rank buildingshttps://projecteuclid.org/euclid.kmj/1530496852<strong>Anton Deitmar</strong>, <strong>Rupert McCallum</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 440--455.</p><p><strong>Abstract:</strong><br/>
We prove a prime geodesic theorem for compact quotients of affine buildings and apply it to get class number asymptotics for global fields of positive characteristic.
</p>projecteuclid.org/euclid.kmj/1530496852_20180701220050Sun, 01 Jul 2018 22:00 EDTA note on families of monogenic number fieldshttps://projecteuclid.org/euclid.kmj/1530496853<strong>Joachim König</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 456--464.</p><p><strong>Abstract:</strong><br/>
We give a sufficient criterion for specializations of certain families of polynomials to yield monogenic number fields. This generalizes constructions in several earlier papers. As applications we give new infinite families of monogenic number fields for several prescribed Galois groups.
</p>projecteuclid.org/euclid.kmj/1530496853_20180701220050Sun, 01 Jul 2018 22:00 EDTEnergy gaps for $p$-Yang-Mills fields over compact Riemannian manifoldshttps://projecteuclid.org/euclid.kmj/1540951247<strong>Zhen-Rong Zhou</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 3, 465--474.</p><p><strong>Abstract:</strong><br/>
In this paper, an inequality of Simons type for $p$-Yang-Mills fields is established over compact Riemannian manifolds, and then, the energy gaps are obtained.
</p>projecteuclid.org/euclid.kmj/1540951247_20181030220129Tue, 30 Oct 2018 22:01 EDTA new formula for the spherical growth series of an amalgamated free product of two infinite cyclic groupshttps://projecteuclid.org/euclid.kmj/1540951250<strong>Michihiko Fujii</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 3, 475--511.</p><p><strong>Abstract:</strong><br/>
We consider a group presented as $G(p,q) = \langle x, y|x^p = y^q\rangle$, with integers $p$ and $q$ satisfying $2 \leq p \leq q$. The group is an amalgamated free product of two infinite cyclic groups and is geometrically realized as the fundamental group of a Seifert fiber space over the 2-dimensional disk with two cone points whose associated cone angles are $\frac{2\pi}{p}$ and $\frac{2\pi}{q}$. We present a formula for the spherical growth series of the group $G(p,q)$ with respect to the generating set $\{x,y,x^{-1}, y^{-1}\}$, from which a rational function expression for the spherical growth series of $G(p,q)$ is derived concretely, once $p$ and $q$ are given. In fact, an elementary computer program constructed from the formula yields an explicit form of a single rational fraction expression for the spherical growth series of $G(p,q)$. Such expressions for several pairs $(p,q)$ appear in this paper. In 1999, C. P. Gill already provided a similar formula for the same group. The formula given here takes a different form from his formula, because the method we used here is independent of that introduced by him.
</p>projecteuclid.org/euclid.kmj/1540951250_20181030220129Tue, 30 Oct 2018 22:01 EDT$q$-series reciprocities and further $\pi$-formulaehttps://projecteuclid.org/euclid.kmj/1540951251<strong>Wenchang Chu</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 3, 512--530.</p><p><strong>Abstract:</strong><br/>
By examining reciprocal relations of basic well-poised, quadratic and cubic series, we establish $q$-analogues of three infinite series for $1/\pi^2$ due to Guillera (2003) and $\lambda$-parameter extensions of three infinite series for $1/\pi$ due to Ramanujan (1914). Several further infinite series identities of Ramanujan-type are also derived as consequences.
</p>projecteuclid.org/euclid.kmj/1540951251_20181030220129Tue, 30 Oct 2018 22:01 EDTArea of the complement of the fast escaping sets of a family of entire functionshttps://projecteuclid.org/euclid.kmj/1540951252<strong>Song Zhang</strong>, <strong>Fei Yang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 3, 531--553.</p><p><strong>Abstract:</strong><br/>
Let $f$ be an entire function with the form $f(z)=P(e^z)/e^z$, where $P$ is a polynomial with $\deg(P)\geq2$ and $P(0)\neq 0$. We prove that the area of the complement of the fast escaping set (hence the Fatou set) of $f$ in a horizontal strip of width $2\pi$ is finite. In particular, the corresponding result can be applied to the sine family $\alpha\sin(z+\beta)$, where $\alpha\neq 0$ and $\beta\in\mathbf{C}$.
</p>projecteuclid.org/euclid.kmj/1540951252_20181030220129Tue, 30 Oct 2018 22:01 EDTHigher Bers maps and Weil-Petersson Teichm\"uller spacehttps://projecteuclid.org/euclid.kmj/1540951253<strong>Shuan Tang</strong>, <strong>Jianjun Jin</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 3, 554--565.</p><p><strong>Abstract:</strong><br/>
It is known that the Bers map, induced by Schwarzian derivative differential operator, is a holomorphic split submersion in Weil-Petersson Teichmüller space. We prove that the higher Bers maps which induced by some higher Schwarzian differential operators in Weil-Petersson Teichmüller space are holomorphic and its differentials at the origin are bounded and surjective.
</p>projecteuclid.org/euclid.kmj/1540951253_20181030220129Tue, 30 Oct 2018 22:01 EDTVojta's conjecture, singularities and multiplier-type idealshttps://projecteuclid.org/euclid.kmj/1540951254<strong>Takehiko Yasuda</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 3, 566--578.</p><p><strong>Abstract:</strong><br/>
We formulate a generalization of Vojta's conjecture in terms of log pairs and variants of multiplier ideals.
</p>projecteuclid.org/euclid.kmj/1540951254_20181030220129Tue, 30 Oct 2018 22:01 EDTDerived category with respect to Gorenstein AC-projective moduleshttps://projecteuclid.org/euclid.kmj/1540951255<strong>Tianya Cao</strong>, <strong>Zhongkui Liu</strong>, <strong>Xiaoyan Yang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 3, 579--590.</p><p><strong>Abstract:</strong><br/>
The aim of this paper is to study the derived category with respect to Gorenstein AC-projective modules. We characterize the bounded Gorenstein AC derived category and obtain some triangle equivalences. We also establish a right recollement related with Gorenstein AC derived category.
</p>projecteuclid.org/euclid.kmj/1540951255_20181030220129Tue, 30 Oct 2018 22:01 EDTOn cobrackets on the Wilson loops associated with flat $\mathrm{GL}(1, \mathbf{R})$-bundles over surfaceshttps://projecteuclid.org/euclid.kmj/1540951256<strong>Moeka Nobuta</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 3, 591--619.</p><p><strong>Abstract:</strong><br/>
Let $S$ be a closed connected oriented surface of genus $g>0$. We study a Poisson subalgebra $W_1(g)$ of $C^{\infty}(\mathrm{Hom}(\pi_1(S), \mathrm{GL}(1, \mathbf{R}))/\mathrm{GL}(1, \mathbf{R}))$, the smooth functions on the moduli space of flat $\mathrm{GL}(1, \mathbf{R})$-bundles over $S$. There is a surjective Lie algebra homomorphism from the Goldman Lie algebra onto $W_1(g)$. We classify all cobrackets on $W_1(g)$ up to coboundary, that is, we compute $H^1(W_1(g), W_1(g) \wedge W_1(g)) \cong \mathrm{Hom}(\mathbf{Z}^{2g}, \mathbf{R})$. As a result, there is no cohomology class corresponding to the Turaev cobracket on $W_1(g)$.
</p>projecteuclid.org/euclid.kmj/1540951256_20181030220129Tue, 30 Oct 2018 22:01 EDT{\L}ojasiewicz exponents of non-degenerate holomorohic and mixed functionshttps://projecteuclid.org/euclid.kmj/1540951257<strong>Mutsuo Oka</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 3, 620--651.</p><p><strong>Abstract:</strong><br/>
We consider {\L}ojasiewicz inequalities for a non-degenerate holomorphic function with an isolated singularity at the origin. We give an explicit estimation of the {\L}ojasiewicz exponent in a slightly weaker form than the assertion in Fukui [10]. We also introduce {\L}ojasiewicz inequality for strongly non-degenerate mixed functions and generalize this estimation for mixed functions.
</p>projecteuclid.org/euclid.kmj/1540951257_20181030220129Tue, 30 Oct 2018 22:01 EDTZariskian adic spaceshttps://projecteuclid.org/euclid.kmj/1540951258<strong>Hiromu Tanaka</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 3, 652--695.</p><p><strong>Abstract:</strong><br/>
We introduce a Zariskian analogue of the theory of Huber's adic spaces.
</p>projecteuclid.org/euclid.kmj/1540951258_20181030220129Tue, 30 Oct 2018 22:01 EDTOn the supersingular divisors of nilpotent admissible indigenous bundleshttps://projecteuclid.org/euclid.kmj/1552982501<strong>Yuichiro Hoshi</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 1, 1--47.</p><p><strong>Abstract:</strong><br/>
In the present paper, we give a characterization of the supersingular divisors [i.e., the zero loci of the Hasse invariants] of nilpotent admissible/ordinary indigenous bundles on hyperbolic curves. By applying the characterization, we also obtain lists of the nilpotent indigenous bundles on certain hyperbolic curves. Moreover, we prove the hyperbolic ordinariness of certain hyperbolic curves.
</p>projecteuclid.org/euclid.kmj/1552982501_20190319040205Tue, 19 Mar 2019 04:02 EDTBiharmonic orbits of isotropy representations of symmetric spaceshttps://projecteuclid.org/euclid.kmj/1552982505<strong>Shinji Ohno</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 1, 48--63.</p><p><strong>Abstract:</strong><br/>
In this paper, we give a necessarly and sufficient condition for orbits of linear isotropy representations of Riemannian symmetric spaces are biharmonic submanifolds in hyperspheres in Euclidean spaces. In particular, we obtain examples of biharmonic submanifolds in hyperspheres whose co-dimension is greater than one.
</p>projecteuclid.org/euclid.kmj/1552982505_20190319040205Tue, 19 Mar 2019 04:02 EDTSome remarks on Riemannian manifolds with parallel Cotton tensorhttps://projecteuclid.org/euclid.kmj/1552982506<strong>Hai-Ping Fu</strong>, <strong>Gao-Bo Xu</strong>, <strong>Yong-Qian Tao</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 1, 64--74.</p><p><strong>Abstract:</strong><br/>
We give some sufficient conditions for stochastically complete Riemannian manifolds with parallel Cotton tensor to be either Einstein or of constant sectional curvature, and obtain an optimal pinching theorem. In particular, when $n$ = 4, we give a full classification.
</p>projecteuclid.org/euclid.kmj/1552982506_20190319040205Tue, 19 Mar 2019 04:02 EDTZariski-van Kampen theorems for singular varieties—an approach via the relative monodromy variationhttps://projecteuclid.org/euclid.kmj/1552982507<strong>Christophe Eyral</strong>, <strong>Peter Petrov</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 1, 75--98.</p><p><strong>Abstract:</strong><br/>
The classical Zariski-van Kampen theorem gives a presentation of the fundamental group of the complement of a complex algebraic curve in $\mathbf{P}^2$. The first generalization of this theorem to singular (quasi-projective) varieties was given by the first author. In both cases, the relations are generated by the standard monodromy variation operators associated with the special members of a generic pencil of hyperplane sections. In the present paper, we give a new generalization in which the relations are generated by the \emph{relative} monodromy variation operators introduced by D. Chéniot and the first author. The advantage of using the relative operators is not only to cover a larger class of varieties but also to unify the Zariski-van Kampen type theorems for the fundamental group and for higher homotopy groups. In the special case of non-singular varieties, the main result of this paper was conjectured by D. Chéniot and the first author.
</p>projecteuclid.org/euclid.kmj/1552982507_20190319040205Tue, 19 Mar 2019 04:02 EDTNote on class number parity of an abelian field of prime conductor, IIhttps://projecteuclid.org/euclid.kmj/1552982508<strong>Humio Ichimura</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 1, 99--110.</p><p><strong>Abstract:</strong><br/>
For a fixed integer $n \geq 1$, let $p=2n\ell+1$ be a prime number with an odd prime number $\ell$, and let $F=F_{p,\ell}$ be the real abelian field of conductor $p$ and degree $\ell$. We show that the class number $h_F$ of $F$ is odd when 2 remains prime in the real $\ell$th cyclotomic field $\mathbf{Q}(\zeta_{\ell})^+$ and $\ell$ is sufficiently large.
</p>projecteuclid.org/euclid.kmj/1552982508_20190319040205Tue, 19 Mar 2019 04:02 EDTde Rham theory and cocycles of cubical sets from smooth quandleshttps://projecteuclid.org/euclid.kmj/1552982509<strong>Takefumi Nosaka</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 1, 111--129.</p><p><strong>Abstract:</strong><br/>
We show a de Rham theorem for cubical manifolds, and study rational homotopy type of the classifying spaces of smooth quandles. We also show that secondary characteristic classes in [8, 9] produce cocycles of quandles.
</p>projecteuclid.org/euclid.kmj/1552982509_20190319040205Tue, 19 Mar 2019 04:02 EDTThe gamma filtrations of $K$-theory of complete flag varietieshttps://projecteuclid.org/euclid.kmj/1552982510<strong>Nobuaki Yagita</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 1, 130--159.</p><p><strong>Abstract:</strong><br/>
Let $G$ be a compact Lie group and $T$ its maximal torus. In this paper, we try to compute $gr_{\gamma}^*(G/T)$ the graded ring associated with the gamma filtration of the complex $K$-theory $K^0(G/T)$. We use the Chow rings of corresponding versal flag varieties.
</p>projecteuclid.org/euclid.kmj/1552982510_20190319040205Tue, 19 Mar 2019 04:02 EDTConformal and projective characterizations of an odd dimensional unit spherehttps://projecteuclid.org/euclid.kmj/1552982511<strong>Ramesh Sharma</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 1, 160--169.</p><p><strong>Abstract:</strong><br/>
We obtain two characterizations of an odd-dimensional unit sphere of dimension $>3$ by proving the following two results: (i) If a complete connected $\eta$-Einstein $K$-contact manifold $M$ of dimension $>3$ admits a conformal vector field $V$, then either $M$ is isometric to a unit sphere, or $V$ is an infinitesimal automorphism of $M$. (ii) If $V$ was a projective vector field in (i), then the same conclusions would hold, except in the first case, $M$ would be locally isometric to a unit sphere.
</p>projecteuclid.org/euclid.kmj/1552982511_20190319040205Tue, 19 Mar 2019 04:02 EDTOn the Chow groups of certain EPW sexticshttps://projecteuclid.org/euclid.kmj/1552982512<strong>Robert Laterveer</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 42, Number 1, 170--201.</p><p><strong>Abstract:</strong><br/>
This note is about the Hilbert square $X=S^{[2]}$, where $S$ is a general $K3$ surface of degree 10, and the anti-symplectic birational involution $\iota$ of $X$ constructed by O'Grady. The main result is that the action of $\iota$ on certain pieces of the Chow groups of $X$ is as expected by Bloch's conjecture. Since $X$ is birational to a double EPW sextic $X^\prime$, this has consequences for the Chow ring of the EPW sextic $Y\subset\mathbf{P}^5$ associated to $X^\prime$.
</p>projecteuclid.org/euclid.kmj/1552982512_20190319040205Tue, 19 Mar 2019 04:02 EDT