Kodai Mathematical Journal Articles (Project 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 EDTReidemeister torsion of a 3-manifold obtained by an integral Dehn-surgery along the figure-eight knothttp://projecteuclid.org/euclid.kmj/1467830138<strong>Teruaki Kitano</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 2, 290--296.</p><p><strong>Abstract:</strong><br/> Let M be a 3-manifold obtained by a Dehn-surgery along the figure-eight knot. We give a formula of the Reidemeisiter torsion of M for any SL (2; C )-irreducible representation. It has a rational expression of the trace of the image of the meridian. </p>projecteuclid.org/euclid.kmj/1467830138_20160706143543Wed, 06 Jul 2016 14:35 EDTThe asymptotic behavior of holomorphic 1-cochainshttp://projecteuclid.org/euclid.kmj/1467830139<strong>Daisuke Yamaki</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 2, 297--317.</p><p><strong>Abstract:</strong><br/> In this paper, we focus on relations between holomorphic 1-forms and holomorphic 1-cochains on a closed Riemann surface. Holomorphic 1-cochains are defined by Wilson in 2008 using a combinatorial Hodge theory. A holomorphic 1-form is characterized by its periods. So is a holomorphic 1-cochain. We consider relations between a holomorphic 1-form and a holomorphic 1-cochain which have the same periods and show that holomorphic 1-cochains provide an approximation of holomorphic 1-forms. </p>projecteuclid.org/euclid.kmj/1467830139_20160706143543Wed, 06 Jul 2016 14:35 EDTSome new lower bounds of the first eigenvalue on Finsler manifoldshttp://projecteuclid.org/euclid.kmj/1467830140<strong>Song-Ting Yin</strong>, <strong>Qun He</strong>, <strong>Da-Xiao Zheng</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 2, 318--339.</p><p><strong>Abstract:</strong><br/> We establish some unified lower bounds for the first Neumann and closed eigenvalues of the Finsler-Laplacian on compact Finsler manifolds under the weighted Ricci curvature conditions, which extend some recent theorems on the first eigenvalue of the Riemannian-Laplacian. Moreover, the Lichnerowicz type lower bound for the first Dirichlet eigenvalue of the Finsler-Laplacian is also obtained. </p>projecteuclid.org/euclid.kmj/1467830140_20160706143543Wed, 06 Jul 2016 14:35 EDTCohomology formula for obstructions to asymptotic Chow semistabilityhttp://projecteuclid.org/euclid.kmj/1467830141<strong>Yuta Suzuki</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 2, 340--353.</p><p><strong>Abstract:</strong><br/> Odaka [16] and Wang [19] proved the intersection formula for the Donaldson-Futaki invariant. In this paper, we generalize this result for the higher Futaki invariants, which are obstructions to asymptotic Chow semistability. </p>projecteuclid.org/euclid.kmj/1467830141_20160706143543Wed, 06 Jul 2016 14:35 EDTA theorem of Liouville type for p -harmonic maps in weighted Riemannian manifoldshttp://projecteuclid.org/euclid.kmj/1467830142<strong>Jian-Feng Zhang</strong>, <strong>Yue Wang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 2, 354--365.</p><p><strong>Abstract:</strong><br/> Let M be a weighted Riemannian manifold with non-negative Bakry-Émery-Ricci curvature and N be a complete Riemannian manifold of non-positive sectional curvature. In this paper, the p -harmonic map u : M → N is studied, and a theorem of Liouville type is obtained. </p>projecteuclid.org/euclid.kmj/1467830142_20160706143543Wed, 06 Jul 2016 14:35 EDTLinear combinations of harmonic quasiconformal mappings convex in one directionhttp://projecteuclid.org/euclid.kmj/1467830143<strong>Yong Sun</strong>, <strong>Antti Rasila</strong>, <strong>Yue-Ping Jiang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 2, 366--377.</p><p><strong>Abstract:</strong><br/> In this paper, we introduce a new class $\mathcal{S}_{H}$ ( k , γ; φ) of harmonic quasiconformal mappings, where k $\in$ [0,1), γ $\in$ [0,π) and φ is an analytic function. Sufficient conditions for the linear combinations of mappings in such classes to be in a similar class, and convex in a given direction, are established. In particular, we prove that the images of linear combinations in this class, for special choices of γ and φ, are convex. </p>projecteuclid.org/euclid.kmj/1467830143_20160706143543Wed, 06 Jul 2016 14:35 EDTA construction of lattices in splittable solvable Lie groupshttp://projecteuclid.org/euclid.kmj/1467830144<strong>Takumi Yamada</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 2, 378--388.</p><p><strong>Abstract:</strong><br/> In this paper, we consider a unified constructions of lattices in splittable solvable Lie groups. </p>projecteuclid.org/euclid.kmj/1467830144_20160706143543Wed, 06 Jul 2016 14:35 EDTOn convexity of simple closed frontalshttp://projecteuclid.org/euclid.kmj/1467830145<strong>Tomonori Fukunaga</strong>, <strong>Masatomo Takahashi</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 2, 389--398.</p><p><strong>Abstract:</strong><br/> We study convexity of simple closed frontals of Legendre curves in the Euclidean plane by using the curvature of Legendre curves. We show that for a Legendre curve, the simple closed frontal under conditions is convex if and only if the sign of both functions of the curvature of the Legendre curve does not change. We also give some examples of convex simple closed frontals. </p>projecteuclid.org/euclid.kmj/1467830145_20160706143543Wed, 06 Jul 2016 14:35 EDTTikhonov regularization for Dunkl multiplier operatorshttp://projecteuclid.org/euclid.kmj/1467830146<strong>Fethi Soltani</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 2, 399--409.</p><p><strong>Abstract:</strong><br/> We study some class of Dunkl multiplier operators T k , m ; and we give for them an application of the theory of reproducing kernels to the Tikhonov regularization, which gives the best approximation of the operators T k , m on the Dunkl-type Paley-Wiener spaces H h . </p>projecteuclid.org/euclid.kmj/1467830146_20160706143543Wed, 06 Jul 2016 14:35 EDTDouady-Earle extension of the strongly symmetric homeomorphismhttp://projecteuclid.org/euclid.kmj/1467830147<strong>Yan Wu</strong>, <strong>Yi Qi</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 2, 410--424.</p><p><strong>Abstract:</strong><br/> It is shown that the complex dilatation of the Douady-Earle extension of a strongly symmetric homeomorphism induces a vanishing Carleson measure on the unit disk D . As application, it is proved that the VMO-Teichmüller space is a subgroup of the universal Teichmüller space. </p>projecteuclid.org/euclid.kmj/1467830147_20160706143543Wed, 06 Jul 2016 14:35 EDTA sharp smoothness of the conjugation of class P-homeomorphisms to diffeomorphismshttp://projecteuclid.org/euclid.kmj/1467830148<strong>Abdelhamid Adouani</strong>, <strong>Habib Marzougui</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 2, 425--438.</p><p><strong>Abstract:</strong><br/> Let f be a class P -homeomorphism of the circle. We prove that there exists a piecewise analytic homeomorphism that conjugate f to a one-class P with prescribed break points lying on pairwise distinct orbits. As a consequence, we give a sharp estimate for the smoothness of a conjugation of class P -homeomorphism f of the circle satisfying the (D)-property (i.e. the product of f -jumps in the break points contained in a same orbit is trivial), to diffeomorphism. When f does not satisfy the (D)-property the conjugating homeomorphism is never a class P and even more it is not absolutely continuous function when the total product of f -jumps in all the break points is non-trivial. </p>projecteuclid.org/euclid.kmj/1467830148_20160706143543Wed, 06 Jul 2016 14:35 EDTBalls in quaternionic hyperbolic manifoldshttp://projecteuclid.org/euclid.kmj/1467830149<strong>Wensheng Cao</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 2, 439--454.</p><p><strong>Abstract:</strong><br/> By use of the Zassenhaus neighborhood of Sp( n ,1), we obtain an explicit lower bound for the radius of the largest inscribed ball in quaternionic hyperbolic n-manifold $\mathcal{M}$ = H H n /Γ. As an application, we obtain a lower bound for the volumes of quaternionic hyperbolic n-manifolds. </p>projecteuclid.org/euclid.kmj/1467830149_20160706143543Wed, 06 Jul 2016 14:35 EDTOn combinatorial criteria for non-degenerate singularitieshttp://projecteuclid.org/euclid.kmj/1467830150<strong>Szymon Brzostowski</strong>, <strong>Grzegorz Oleksik</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 2, 455--468.</p><p><strong>Abstract:</strong><br/> In this article we give a sufficient and necessary condition for a Kouchnirenko non-degenerate holomorphic function to have an isolated singularity at 0 in terms of its support. As a corollary we give some useful sufficient conditions for singularity to be isolated. </p>projecteuclid.org/euclid.kmj/1467830150_20160706143543Wed, 06 Jul 2016 14:35 EDTRicci tensors on three-dimensional almost coKähler manifoldshttp://projecteuclid.org/euclid.kmj/1478073764<strong>Yaning Wang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 3, 469--483.</p><p><strong>Abstract:</strong><br/> Let M 3 be a three-dimensional almost coKähler manifold such that the Ricci curvature of the Reeb vector field is invariant along the Reeb vector field. In this paper, we obtain some classification results of M 3 for which the Ricci tensor is η-parallel or the Riemannian curvature tensor is harmonic. </p>projecteuclid.org/euclid.kmj/1478073764_20161102040322Wed, 02 Nov 2016 04:03 EDTA formula for the algebraic degree in semidefinite programminghttp://projecteuclid.org/euclid.kmj/1478073765<strong>Dang Tuan Hiep</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 3, 484--488.</p><p><strong>Abstract:</strong><br/> In this paper we use the Bott residue formula in equivariant cohomology to show a formula for the algebraic degree in semidefinite programming. </p>projecteuclid.org/euclid.kmj/1478073765_20161102040322Wed, 02 Nov 2016 04:03 EDTRigidity of closed metric measure spaces with nonnegative curvaturehttp://projecteuclid.org/euclid.kmj/1478073766<strong>Jia-Yong Wu</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 3, 489--499.</p><p><strong>Abstract:</strong><br/> We show that one-dimensional circle is the only case for closed smooth metric measure spaces with nonnegative Bakry-Émery Ricci curvature whose spectrum of the weighted Laplacian has an optimal positive upper bound. This result extends the work of Hang-Wang in the manifold case (Int. Math. Res. Not. 18 (2007), Art. ID rnm064, 9pp). </p>projecteuclid.org/euclid.kmj/1478073766_20161102040322Wed, 02 Nov 2016 04:03 EDTNotes on the value distribution of ff ( k ) - bhttp://projecteuclid.org/euclid.kmj/1478073767<strong>Weiran Lü</strong>, <strong>Nana Liu</strong>, <strong>Chungchun Yang</strong>, <strong>Caiping Zhuo</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 3, 500--509.</p><p><strong>Abstract:</strong><br/> Let f denote a transcendental meromorphic function with N ( r , f ) = S ( r , f ) and k be an integer. By using methods different from others, we have been able to derive several new results and pose some new conjectures that relate to the yet to be resolved conjecture concerning the quantitative estimates on the zeros of ff ( k ) - b , for a non-vanishing small function b . </p>projecteuclid.org/euclid.kmj/1478073767_20161102040322Wed, 02 Nov 2016 04:03 EDTOn a certain family of asymmetric Riemann surfaces with the cyclic automorphism grouphttp://projecteuclid.org/euclid.kmj/1478073768<strong>Ewa Kozłowska-Walania</strong>, <strong>Ewa Tyszkowska</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 3, 510--520.</p><p><strong>Abstract:</strong><br/> A compact Riemann surface X of genus g ≥ 2 is called asymmetric or pseudo-real if it admits an anticonformal automorphism but no anticonformal involution. The order d = #(δ) of an anticonformal automorphism δ of such a surface is divisible by 4. In the particular case where d = 4, δ is a pseudo-symmetry and the surface is called pseudo-symmetric . A Riemann surface X is said to be p-hyperelliptic if it admits a conformal involution ρ for which the orbit space X /<ρ> has genus p . This notion is the particular case of so called cyclic ( q , n )- gonal surface which is defined as the one admitting a conformal automorphism φ of prime order n such that X /φ has genus q . We are interested in possible values of n and q for which an asymmetric surface of given genus g ≥ 2 is ( q , n )-gonal, and possible values of p for which the surface is p -hyperelliptic. Up till now, this problem was solved in the case where the surface is asymmetric and pseudo-symmetric. If an asymmetric Riemann surface X is not pseudo-symmetric then any anticonformal automorphism of X has order divisible by 2 s n for s ≥ 3 and n = 1 or n being an odd prime. In this paper we give the necessary and sufficient conditions on the existence of an asymmetric Riemann surface with the full automorphism group being G = Z 2 s n , and we study ( q , n )-gonal automorphisms and p -hyperelliptic involutions in G . </p>projecteuclid.org/euclid.kmj/1478073768_20161102040322Wed, 02 Nov 2016 04:03 EDTOn the isometries from the unit disk to infinite dimensional Teichmüller spaceshttp://projecteuclid.org/euclid.kmj/1478073769<strong>Hiromi Ohtake</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 3, 521--529.</p><p><strong>Abstract:</strong><br/> We generalize Earle-Li's polydisk theorem and embedding theorem, and study isometries from the unit disk to infinite dimensional Teichmüller spaces. We also give a simple proof that for any non-Strebel point τ, there exist infinitely many real analytic geodesic disks through τ and the basepoint in infinitely dimensional Teichmüller spaces. </p>projecteuclid.org/euclid.kmj/1478073769_20161102040322Wed, 02 Nov 2016 04:03 EDTSubgroups of the Torelli group generated by two symmetric bounding pair mapshttp://projecteuclid.org/euclid.kmj/1478073770<strong>Michał Stukow</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 3, 530--534.</p><p><strong>Abstract:</strong><br/> Let { a , b } and { c , d } be two pairs of bounding simple closed curves on an oriented surface which intersect nontrivialy. We prove that if these pairs are invariant under the action of an orientation reversing involution, then the corresponding bounding pair maps generate a free group. This supports the conjecture stated by C. Leininger and D. Margalit that any pair of elements of the Torelli group either commute or generate a free group. </p>projecteuclid.org/euclid.kmj/1478073770_20161102040322Wed, 02 Nov 2016 04:03 EDTWell-posedness and decay property for the generalized damped Boussinesq equation with double rotational inertiahttp://projecteuclid.org/euclid.kmj/1478073771<strong>Zaiyun Zhang</strong>, <strong>Jianhua Huang</strong>, <strong>Mingbao Sun</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 3, 535--551.</p><p><strong>Abstract:</strong><br/> In this paper, we investigate the initial value problem (IVP henceforth) associated with the generalized damped Boussinesq equation with double rotational inertia $$\left\{\begin{array}{ll} u_{tt}+\gamma\Delta^2 u_{tt}-a\Delta u_{tt}-2b\Delta u_t-\alpha\Delta^3u+\beta\Delta^2 u-\Delta u=\Delta f(u),\quad x \in\mathbb{R}^n, \; t<0, \\ u(x,0)=u_0(x),\quad u_t(x,0)=u_1(x),\quad x \in\mathbb{R}^n. \end{array}\right.$$ Based on decay estimates of solutions to the corresponding linear equation, we establish the decay estimates and the pointwise estimates by using Fourier transform. Under small condition on the initial data, we obtain the existence and asymptotic behavior of global solutions in the corresponding Sobolev spaces by time weighted norms technique and the contraction mapping principle. </p>projecteuclid.org/euclid.kmj/1478073771_20161102040322Wed, 02 Nov 2016 04:03 EDTHypersurfaces in Euclidean spaces with finite total curvaturehttp://projecteuclid.org/euclid.kmj/1478073772<strong>Peng Zhu</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 3, 552--566.</p><p><strong>Abstract:</strong><br/> We discuss complete noncompact hypersurfaces in the Euclidean space R n +1 with finite total curvature. We obtain vanishing result and finiteness theorem for the space of L 2 harmonic 2-forms. These results are generalized versions of results for L 2 harmonic 1-forms. </p>projecteuclid.org/euclid.kmj/1478073772_20161102040322Wed, 02 Nov 2016 04:03 EDTOn p -biharmonic submanifolds in nonpositively curved manifoldshttp://projecteuclid.org/euclid.kmj/1478073773<strong>Xiangzhi Cao</strong>, <strong>Yong Luo</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 3, 567--578.</p><p><strong>Abstract:</strong><br/> Let u : ( M , g ) → ( N , h ) be a map between Riemannian manifolds ( M , g ) and ( N , h ). The p -bienergy of u is τ p ( u ) = ∫ M |τ( u )| p dν g , where τ( u ) is the tension field of u and p > 1. Critical points of τ p are called p -biharmonic maps and isometric p -biharmonic maps are called p -biharmonic submanifolds. When p = 2, p -biharmonic submanifolds are biharmonic submanifolds and in recent years many nonexistence results are found for biharmonic submanifolds in nonpositively curved manifolds. In this paper we will study the nonexistence result for general p -biharmonic submanifolds. </p>projecteuclid.org/euclid.kmj/1478073773_20161102040322Wed, 02 Nov 2016 04:03 EDTCurved folding and planar cutting of simple closed curve on a conical origamihttp://projecteuclid.org/euclid.kmj/1478073774<strong>Ikhan Choi</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 3, 579--595.</p><p><strong>Abstract:</strong><br/> The fold-and-cut theorem states that one can find a flat folding of paper, so that one complete straight cut on the folding creates any desired polygon. We extend this problem to curved origami for piecewise C 1 simple closed curves. Many of those curves on paper turn out to be cut by a straight plane after we fold the paper into a conical shape —the surface consists of half-lines with a common vertex. Let γ: I → R 2 be a piecewise C 1 simple closed curve such that there exists a parametrization γ(ψ)= (r(ψ) cos ψ, r (ψ) sin ψ) on ψ $\in$ [0,2π) for a Lipschitz continuous function r : R → (0, ∞). We prove that there exists a conical folding of the plane so that γ can be cut by a plane on the folding if a certain condition on angular total variation holds. </p>projecteuclid.org/euclid.kmj/1478073774_20161102040322Wed, 02 Nov 2016 04:03 EDTSublinear tracking in Thurston's metric for random walkshttp://projecteuclid.org/euclid.kmj/1478073775<strong>Huiping Pan</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 3, 596--614.</p><p><strong>Abstract:</strong><br/> In this paper, we prove the sublinear tracking property in Thurston's metric for sample paths of random walks on mapping class group. </p>projecteuclid.org/euclid.kmj/1478073775_20161102040322Wed, 02 Nov 2016 04:03 EDTExtrinsic circular trajectories on totally η-umbilic real hypersurfaces in a complex hyperbolic spacehttp://projecteuclid.org/euclid.kmj/1478073776<strong>Tuya Bao</strong>, <strong>Toshiaki Adachi</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 39, Number 3, 615--631.</p><p><strong>Abstract:</strong><br/> A trajectory for a Sasakian magnetic field, which is a generalization of geodesics, on a real hypersurface in a complex hyperbolic space C H n is said to be extrinsic circular if it can be regarded as a circle as a curve in C H n . We study how the moduli space of extrinsic circular trajectories, which is the set of their congruence classes, on a totally η-umbilic real hypersurface is contained in the moduli space of circles in C H n . From this aspect we characterize tubes around totally geodesic complex hypersurfaces C H n -1 in C H n by some properties of such trajectories. </p>projecteuclid.org/euclid.kmj/1478073776_20161102040322Wed, 02 Nov 2016 04:03 EDTComplete flat resolutions, Tate homology and the depth formulahttp://projecteuclid.org/euclid.kmj/1490083219<strong>Yanping Liu</strong>, <strong>Zhongkui Liu</strong>, <strong>Xiaoyan Yang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 1, 1--15.</p><p><strong>Abstract:</strong><br/> We introduce Tate homology of complexes of finite Gorenstein flat dimension based on complete flat resolutions and give a new method of computing Tate homology in Christensen and Jorgensen's sense. We also investigate the relationship between Tate homology and Tate cohomology. As an application, a more brief proof of the main result on derived depth formula of [Vanishing of Tate homology and depth formula over local rings, J. Pure Appl. Algebra 219 (2015) 464-481] is given. </p>projecteuclid.org/euclid.kmj/1490083219_20170321040117Tue, 21 Mar 2017 04:01 EDTA number theoretical observation of a resonant interaction of Rossby waveshttp://projecteuclid.org/euclid.kmj/1490083220<strong>Nobu Kishimoto</strong>, <strong>Tsuyoshi Yoneda</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 1, 16--20.</p><p><strong>Abstract:</strong><br/> Rossby waves are generally expected to dominate the β plane dynamics in geophysics, and here in this paper we give a number theoretical observation of the resonant interaction with a Diophantine equation. The set of resonant frequencies does not have any frequency on the horizontal axis. </p>projecteuclid.org/euclid.kmj/1490083220_20170321040117Tue, 21 Mar 2017 04:01 EDTCentro-affine invariants and the canonical Lorentz metric on the space of centered ellipseshttp://projecteuclid.org/euclid.kmj/1490083221<strong>Marcos Salvai</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 1, 21--30.</p><p><strong>Abstract:</strong><br/> We consider smooth plane curves which are convex with respect to the origin. We describe centro-affine invariants (that is, GL + (2, R )-invariants), such as centro-affine curvature and arc length, in terms of the canonical Lorentz structure on the three dimensional space of all the ellipses centered at zero, by means of null curves of osculating ellipses. This is the centro-affine analogue of the approach to conformal invariants of curves in the sphere introduced by Langevin and O'Hara, using the canonical pseudo Riemannian metric on the space of circles. </p>projecteuclid.org/euclid.kmj/1490083221_20170321040117Tue, 21 Mar 2017 04:01 EDTHerz-type Besov spaces of variable smoothness and integrabilityhttp://projecteuclid.org/euclid.kmj/1490083222<strong>Douadi Drihem</strong>, <strong>Rabah Heraiz</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 1, 31--57.</p><p><strong>Abstract:</strong><br/> In this paper, Herz-type Besov spaces with variable smoothness and integrability are introduced. Our scale contains variable Besov spaces as special cases. We prove several basic properties, especially the Sobolev-type embeddings. </p>projecteuclid.org/euclid.kmj/1490083222_20170321040117Tue, 21 Mar 2017 04:01 EDTOn Faltings' local-global principle of generalized local cohomology moduleshttp://projecteuclid.org/euclid.kmj/1490083223<strong>Nguyen Van Hoang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 1, 58--62.</p><p><strong>Abstract:</strong><br/> Let R be a commutative Noetherian ring, I an ideal of R and M , N finitely generated R -modules. Let 0 ≤ n $\in$ Z . This note shows that the least integer i such that dim Supp( $H^i_I$ ( M , N )/ K ) ≥ n for any finitely generated submodule K of $H^i_I$ ( M , N ) equal to the number inf{ $f_{I_\frak{p}}(M_\frak{p},N_\frak{p})$ | $\frak{p}$ $\in$ Supp( N / I M N ), dim R / $\frak{p}$ ≥ n }, where $f_{I_\frak{p}}(M_\frak{p},N_\frak{p})$ is the least integer i such that $H^i_{I_\frak{p}}(M_{\frak{p}},N_{\frak{p}})$ is not finitely generated, and I M = ann( M / IM ). This extends the main result of Asadollahi-Naghipour [1] and Mehrvarz-Naghipour-Sedghi [8] for generalized local cohomology modules by a short proof. </p>projecteuclid.org/euclid.kmj/1490083223_20170321040117Tue, 21 Mar 2017 04:01 EDTGlobal attractors for a Kirchhoff type plate equation with memoryhttp://projecteuclid.org/euclid.kmj/1490083224<strong>Xiaobin Yao</strong>, <strong>Qiaozhen Ma</strong>, <strong>Ling Xu</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 1, 63--78.</p><p><strong>Abstract:</strong><br/> A Kirchhoff type plate equation with memory is investigated. Under the suitable assumptions, we establish the existence of a global attractor by using the contraction function method. </p>projecteuclid.org/euclid.kmj/1490083224_20170321040117Tue, 21 Mar 2017 04:01 EDTThe Euler product for the Riemann zeta-function in the critical striphttp://projecteuclid.org/euclid.kmj/1490083225<strong>Hirotaka Akatsuka</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 1, 79--101.</p><p><strong>Abstract:</strong><br/> In this paper we study a pointwise asymptotic behavior of the partial Euler product for the Riemann zeta-function on the right half of the critical strip. We discuss relations among the behavior of the partial Euler product, the distribution of the prime numbers and the distribution of nontrivial zeros of the Riemann zeta-function. </p>projecteuclid.org/euclid.kmj/1490083225_20170321040117Tue, 21 Mar 2017 04:01 EDTUnit tangent sphere bundles with the Reeb flow invariant Ricci operatorhttp://projecteuclid.org/euclid.kmj/1490083226<strong>Jong Taek Cho</strong>, <strong>Sun Hyang Chun</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 1, 102--116.</p><p><strong>Abstract:</strong><br/> In this paper, we study unit tangent sphere bundles T 1 M whose Ricci operator $\bar{S}$ is Reeb flow invariant, that is, L ξ $\bar{S}$ = 0. We prove that for a 3-dimensional Riemannian manifold M , T 1 M satisfies L ξ $\bar{S}$ = 0 if and only if M is of constant curvature 1. Also, we prove that for a 4-dimensional Riemannian manifold M , T 1 M satisfies L ξ $\bar{S}$ = 0 and ℓ $\bar{S}$ ξ = 0 if and only if M is of constant curvature 1 or 2, where ℓ = $\bar{R}$ (·,ξ)ξ is the characteristic Jacobi operator. </p>projecteuclid.org/euclid.kmj/1490083226_20170321040117Tue, 21 Mar 2017 04:01 EDTGlobal uniqueness results for ground states for a class of quasilinear elliptic equationshttp://projecteuclid.org/euclid.kmj/1490083227<strong>Shinji Adachi</strong>, <strong>Masataka Shibata</strong>, <strong>Tatsuya Watanabe</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 1, 117--142.</p><p><strong>Abstract:</strong><br/> In this paper, we are concerned with the uniqueness of ground states for a class of quasilinear elliptic equations which arise in the study of plasma physics. We obtain global uniqueness results in the sense that we don't require any assumptions on the parameter. </p>projecteuclid.org/euclid.kmj/1490083227_20170321040117Tue, 21 Mar 2017 04:01 EDTEffective actions of the general indefinite unitary groups on holomorphically separable manifoldshttp://projecteuclid.org/euclid.kmj/1490083228<strong>Yoshikazu Nagata</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 1, 143--177.</p><p><strong>Abstract:</strong><br/> We determine all holomorphically separable complex manifolds of dimension p + q which admit smooth envelopes of holomorphy and effective general indefinite unitary group actions of size p + q . Also we give exact description of the automorphism groups of those complex manifolds. As an application we consider a characterization of those complex manifolds by their automorphism groups. </p>projecteuclid.org/euclid.kmj/1490083228_20170321040117Tue, 21 Mar 2017 04:01 EDTRelative purity in log étale cohomologyhttp://projecteuclid.org/euclid.kmj/1490083229<strong>Kazumi Higashiyama</strong>, <strong>Takashi Kamiya</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 1, 178--183.</p><p><strong>Abstract:</strong><br/> We study log étale cohomology. The goal is to prove relative purity in log étale cohomology. </p>projecteuclid.org/euclid.kmj/1490083229_20170321040117Tue, 21 Mar 2017 04:01 EDTA note on "On the appearance of Eisenstein series through degeneration"http://projecteuclid.org/euclid.kmj/1499846592<strong>Thérèse Falliero</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 185--199.</p><p><strong>Abstract:</strong><br/> Let M = Γ $\backslash$ H be a geometrically finite hyperbolic surface, realized as the quotient of the hyperbolic upper half plane H by a geometrically finite discrete group of isometries acting on H . To a parabolic element of the uniformizing group Γ, there is an associated 1-form parabolic Eisenstein series. To a primitive hyperbolic element, then, following ideas due to Kudla-Millson, there is a corresponding 1-form hyperbolic Eisenstein series. In this article, we study the limiting behavior of these hyperbolic Eisenstein series on a degenerating family of hyperbolic Riemann surfaces of finite type, using basically the limiting behavior of counting functions associated to degenerating hyperbolic Riemann surfaces. In this sense, we generalize the results obtained in Garbin, Jorgenson and Munn (Comment Math Helv 83:701-721, 2008) to the case of geometrically finite hyperbolic surfaces of infinite volume and form-valued parabolic and hyperbolic Eisenstein series. </p>projecteuclid.org/euclid.kmj/1499846592_20170712040345Wed, 12 Jul 2017 04:03 EDTCriteria for singularities for mappings from two-manifold to the plane. The number and signs of cuspshttp://projecteuclid.org/euclid.kmj/1499846594<strong>Iwona Krzyżanowska</strong>, <strong>Aleksandra Nowel</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 200--213.</p><p><strong>Abstract:</strong><br/> Let M $subset$ R n +2 be a two-dimensional complete intersection. We show how to check whether a mapping f : M → R 2 is 1-generic with only folds and cusps as singularities. In this case we give an effective method to count the number of positive and negative cusps of a polynomial f , using the signatures of some quadratic forms. </p>projecteuclid.org/euclid.kmj/1499846594_20170712040345Wed, 12 Jul 2017 04:03 EDTLinear Weingarten submanifolds immersed in a space formhttp://projecteuclid.org/euclid.kmj/1499846595<strong>Henrique Fernandes De Lima</strong>, <strong>Fábio Reis Dos Santos</strong>, <strong>Jogli Gidel Da Silva Araújo</strong>, <strong>Marco Antonio Lázaro Velásquez</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 214--228.</p><p><strong>Abstract:</strong><br/> In this paper, we deal with complete linear Weingarten submanifolds M n immersed with parallel normalized mean curvature vector field in a Riemannian space form Q c n + p of constant sectional curvature c . Under an appropriated restriction on the norm of the traceless part of the second fundamental form, we show that such a submanifold M n must be either totally umbilical or isometric to a Clifford torus, if c = 1, a circular cylinder, if c = 0, or a hyperbolic cylinder, if c = −1. We point out that our results are natural generalizations of those ones obtained in [2] and [6]. </p>projecteuclid.org/euclid.kmj/1499846595_20170712040345Wed, 12 Jul 2017 04:03 EDTUniversal inequalities for eigenvalues of a class of operators on Riemannian manifoldhttp://projecteuclid.org/euclid.kmj/1499846596<strong>Jianghai Shi</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 229--253.</p><p><strong>Abstract:</strong><br/> In this paper, we investigate the boundary value problem of the following operator $\left\{\begin{array}{l}\Delta^{2}u-a\rm div\it A\nabla{u}+Vu=\rho\lambda{u}\ \ \hbox{in} \ \rm\Omega, \\ u|_{\partial \Omega}=\frac{\partial u}{\partial v}|_{\partial \Omega}=0,\\ \end{array}\right.$$ where Ω is a bounded domain in an n -dimensional complete Riemannian manifold M n , A is a positive semidefinite symmetric (1,1)-tensor on M n , V is a non-negative continuous function on Ω, v denotes the outwards unit normal vector field of ∂Ω and ρ is a weight function which is positive and continuous on Ω. By the Rayleigh-Ritz inequality, we obtain universal inequalities for the eigenvalues of these operators on bounded domain of complete manifolds isometrically immersed in a Euclidean space, and of complete manifolds admitting special functions which include the Hadamard manifolds with Ricci curvature bounded below, a class of warped product manifolds, the product of Euclidean spaces with any complete manifold and manifolds admitting eigenmaps to a sphere. </p>projecteuclid.org/euclid.kmj/1499846596_20170712040345Wed, 12 Jul 2017 04:03 EDTOpial and Lyapunov inequalities on time scales and their applications to dynamic equationshttp://projecteuclid.org/euclid.kmj/1499846597<strong>Nguyen Du Vi Nhan</strong>, <strong>Tran Dinh Phung</strong>, <strong>Dinh Thanh Duc</strong>, <strong>Vu Kim Tuan</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 254--277.</p><p><strong>Abstract:</strong><br/> We prove some weighted inequalities for delta derivatives acting on products and compositions of functions on time scales and apply them to obtain generalized dynamic Opial-type inequalities. We also employ these inequalities to establish some new dynamic Lyapunov-type inequalities, which are essential in studying disfocality, disconjugacy, lower bounds of eigenvalues, and distance between generalized zeros for half-linear dynamic equations. In particular, we solve an open problem posed by Saker in [Math. Comput. Modelling 58 (2013), 1777-1790]. Moreover, the results presented in this paper generalize, improve, extend, and unify most of known results not only in the discrete and continuous analysis but also on time scales. </p>projecteuclid.org/euclid.kmj/1499846597_20170712040345Wed, 12 Jul 2017 04:03 EDTA technique of constructing planar harmonic mappings and their propertieshttp://projecteuclid.org/euclid.kmj/1499846598<strong>Om P. Ahuja</strong>, <strong>Sumit Nagpal</strong>, <strong>V. Ravichandran</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 278--288.</p><p><strong>Abstract:</strong><br/> The analytic part of a planar harmonic mapping plays a vital role in shaping its geometric properties. For a normalized analytic function f defined in the unit disk, define an operator Φ[ f ]( z ) = f ( z ) + $\overline{f(z)-z}$ . In this paper, necessary and sufficient conditions on f are determined for the harmonic function Φ[ f ] to be univalent and convex in one direction. Similar results are obtained for Φ[ f ] to be starlike and convex in the unit disk. This results in the coefficient estimates, growth results and convolution properties of Φ[ f ]. In addition, various radii constants associated with Φ[ f ] have been computed. </p>projecteuclid.org/euclid.kmj/1499846598_20170712040345Wed, 12 Jul 2017 04:03 EDTRate functions for random walks on random conductance models and related topicshttp://projecteuclid.org/euclid.kmj/1499846599<strong>Chikara Nakamura</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 289--321.</p><p><strong>Abstract:</strong><br/> We consider laws of the iterated logarithm and the rate function for sample paths of random walks on random conductance models under the assumption that the random walks enjoy long time sub-Gaussian heat kernel estimates. </p>projecteuclid.org/euclid.kmj/1499846599_20170712040345Wed, 12 Jul 2017 04:03 EDTA note on the asymptotic behavior of conformal metrics with negative curvatures near isolated singularitieshttp://projecteuclid.org/euclid.kmj/1499846600<strong>Tanran Zhang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 322--342.</p><p><strong>Abstract:</strong><br/> The asymptotic behavior of conformal metrics with negative curvatures near an isolated singularity was described up to the second order derivatives by Kraus and Roth, 2008. We refine Kraus and Roth's result for the second order mixed derivatives and give estimates for higher order derivatives near an isolated singularity. We also compute the Minda-type limits for SK-metrics near the singularity. Combining these limits with Ahlfors' lemma, we provide two observations for SK-metrics. </p>projecteuclid.org/euclid.kmj/1499846600_20170712040345Wed, 12 Jul 2017 04:03 EDTp -harmonic functions on complete manifolds with a weighted Poincaré inequalityhttp://projecteuclid.org/euclid.kmj/1499846601<strong>Bui Van Binh</strong>, <strong>Nguyen Thac Dung</strong>, <strong>Nguyen Thi Le Hai</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 343--357.</p><p><strong>Abstract:</strong><br/> In this paper, we consider p -harmonic functions on complete Riemannian manifolds and give different proofs of some main theorems by Chang-Chen-Wei, in [3]. Moreover, we are able to refine their results in case of weakly p -harmonic functions. Some applications to study the connectedness at infinity of stable minimal hypersurfaces are also given. </p>projecteuclid.org/euclid.kmj/1499846601_20170712040345Wed, 12 Jul 2017 04:03 EDTApparent contours of stable maps between closed surfaceshttp://projecteuclid.org/euclid.kmj/1499846602<strong>Takahiro Yamamoto</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 358--378.</p><p><strong>Abstract:</strong><br/> Let M and N be connected and orientable, closed surfaces. For a stable map φ : M → N , denote by c (φ) and n (φ) the numbers of cusps and nodes of φ respectively. In this paper, we determine the minimal number c (φ) + n (φ) among the apparent contours of degree d stable maps M → N whose singular points set consists of one component. </p>projecteuclid.org/euclid.kmj/1499846602_20170712040345Wed, 12 Jul 2017 04:03 EDTOn deviations, small functions and strong asymptotic functions of meromorphic functionshttp://projecteuclid.org/euclid.kmj/1499846603<strong>Ewa Ciechanowicz</strong>, <strong>Ivan Ivanovich Marchenko</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 379--404.</p><p><strong>Abstract:</strong><br/> The paper addresses two long-standing problems: of extending the second main theorem of Nevanlinna to the case of small functions, and of finding an upper limit for the number of asymptotic functions of a function of finite lower order. Upper estimates of the sum of deviations and the numbers of strong asymptotic functions and strong functional asymptotic spots of meromorphic functions of finite lower order are presented. The structure of the set of Petrenko's deviations from small functions for meromorphic functions of finite lower order is examined. An analogue of Denjoy's question for strong asymptotic small functions of meromorphic functions of finite lower order is also considered. </p>projecteuclid.org/euclid.kmj/1499846603_20170712040345Wed, 12 Jul 2017 04:03 EDTL 2 continuity of the Calderón type commutator for the Littlewood-Paley operator with rough variable kernelhttps://projecteuclid.org/euclid.kmj/1509415223<strong>Yanping Chen</strong>, <strong>Zhendong Niu</strong>, <strong>Liwei Wang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 405--420.</p><p><strong>Abstract:</strong><br/>
For b $\in$ Lip ( R n ), the Calderón type commutator for the Littlewood-Paley operator with variable kernel is defined by
μ Ω,1; b ( f )( x ) = $\bigg(\int_0^{\infty}\bigg|\frac{1}{t^2}\int_{|x-y|\leq t}\frac{\Omega(x,x-y)}{|x-y|^{n-1}}(b(x)-b(y))f(y)dy\bigg|^2\frac{dt}{t}\bigg)^{1/2}$ .
By giving a method based on Littlewood-Paley theory, Fourier transform and the spherical harmonic development, we prove the L 2 norm inequalities for the rough operators μ Ω,1; b with Ω( x , z ′) $\in$ L ∞ ( R n ) × L q ( S n −1 ) $(q>\frac{2(n-1)}{n})$ satisfying certain cancellation conditions.
</p>projecteuclid.org/euclid.kmj/1509415223_20171030220055Mon, 30 Oct 2017 22:00 EDTOn proper holomorphic self-mappings of generalized complex ellipsoids and generalized Hartogs triangleshttps://projecteuclid.org/euclid.kmj/1509415224<strong>Akio Kodama</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 421--449.</p><p><strong>Abstract:</strong><br/>
In this paper, we study proper holomorphic self-mappings of generalized complex ellipsoids and generalized Hartogs triangles. By making use of our previous result on the holomorphic automorphism group of a generalized complex ellipsoid and Monti-Morbidelli's result on the extendability of a local CR-diffeomorphism between open subsets contained in the strictly pseudoconvex part of the boundary of a generalized complex ellipsoid, we obtain natural generalizations of some results due to Landucci, Chen-Xu and Zapalowski.
</p>projecteuclid.org/euclid.kmj/1509415224_20171030220055Mon, 30 Oct 2017 22:00 EDTInstability of solitary waves for a generalized derivative nonlinear Schrödinger equation in a borderline casehttps://projecteuclid.org/euclid.kmj/1509415227<strong>Noriyoshi Fukaya</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 450--467.</p><p><strong>Abstract:</strong><br/>
We study the orbital instability of solitary waves for a derivative nonlinear Schrödinger equation with a general nonlinearity. We treat a borderline case between stability and instability, which is left as an open problem by Liu, Simpson and Sulem (2013). We give a sufficient condition for instability of a two-parameter family of solitary waves in a degenerate case by extending the results of Ohta (2011), and verify this condition for some cases.
</p>projecteuclid.org/euclid.kmj/1509415227_20171030220055Mon, 30 Oct 2017 22:00 EDTAn addition type formula for the double cotangent functionhttps://projecteuclid.org/euclid.kmj/1509415228<strong>Masaki Kato</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 468--491.</p><p><strong>Abstract:</strong><br/>
In this paper, we prove an addition type formula for the double cotangent function. Furthermore, we see that the addition theorem of the usual cotangent function, the reciprocity laws of (classical and higher) Dedekind sums, Lerch's functional equation and Ramanujan's formula can be deduced from it.
</p>projecteuclid.org/euclid.kmj/1509415228_20171030220055Mon, 30 Oct 2017 22:00 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 EDT