Faculty Profiles - NAYATANI, Shin

Papers - NAYATANI, Shin

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Maximization of the first Laplace eigenvalue of a finite graph

Gomyou, T; Nayatani, S

LINEAR ALGEBRA AND ITS APPLICATIONS Vol. 720 page： 72 - 90 2025.9

Embedding and the first Laplace eigenvalue of a finite graph

Gomyou, T; Kobayashi, T; Kondo, T; Nayatani, S

JOURNAL OF COMBINATORIAL OPTIMIZATION Vol. 48 ( 1 ) 2024.8

Metrics on a closed surface of genus two which maximize the first eigenvalue of the Laplacian Open Access

Nayatani Shin, Shoda Toshihiro

COMPTES RENDUS MATHEMATIQUE Vol. 357 ( 1 ) page： 84 - 98 2019.1

Fixed-point property for affine actions on a Hilbert space Invited Reviewed Open Access

Shin Nayatani

Vol. B66 page： 115-131 2017

Authorship：Lead author Language：English Publishing type：Research paper (scientific journal)

Gromov showed that for fixed, arbitrarily large C, any uniformly C-Lipschitz affine action of a random group in his graph model on a Hilbert space has a fixed point. We announce a theorem stating that more general affine actions of the same random group on a Hilbert space have a fixed point. We discuss some aspects of the proof.

Open Access

Almost CR structure on the twistor space of a quaternionic CR manifold Invited Reviewed

Hiroyuki Kamada, Shin Nayatani

Current developments in differential geomerty and its elated fields page： 93-114 2016

*Quaternionic CR Geometry Reviewed

Hiroyuki Kamada, Shin Nayatani

Hokkaido Mathematical Journal Vol. 42 page： 1-49 2013

Authorship：Lead author Language：English Publishing type：Research paper (scientific journal)

Modelled on a real hypersurface in a quaternionic manifold, we introduce a quaternionic analogue of CR structure, called quaternionic CR structure. We define the strong pseudoconvexity of this structure as well as the notion of quaternionic pseudohermitian structure. Following the construction of the Tanaka-Webster connection in complex CR geometry, we construct a canonical connection associated with a quaternionic pseudohermitian structure, when the underlying quaternionic CR structure satisfies the ultra-pseudoconvexity which is stronger than the strong pseudoconvexity. Comparison to Biquard's quaternionic contact structure is also made.

N-step energy of maps and the fixed-point property of random groups Reviewed Open Access

Shin Nayatani, Hiroyasu Izeki, Takefumi Kondo

Groups, Geometry, and Dynamics Vol. 6 ( 4 ) page： 701--736 2012

Authorship：Lead author Language：English Publishing type：Research paper (scientific journal)

We prove that a random group of the graph model associated with a sequence of
expanders has the fixed-point property for a certain class of CAT.0/ spaces. We use Gromov's
criterion for the fixed-point property in terms of the growth of n-step energy of equivariant
maps from a finitely generated group into a CAT.0/ space, for which we give a detailed proof.
We estimate a relevant geometric invariant of the tangent cones of the Euclidean buildings
associated with the groups PGL.m;Qr /, and deduce from the general result above that the
same random group has the fixed-point property for all of these Euclidean buildings with m
bounded from above.

DOI： 10.4171/GGD/171

Fixed-point property of random groups Reviewed

Shin Nayatani, Hiroyasu Izeki, Takefumi Kondo

Annals of Global Analysis and Geometry Vol. 35 ( 4 ) page： 363-379 2009

A fixed-point theorem for discrete-group actions on Hadamard spaces Open Access

Vol. 1492 page： 56-64 2006

調和写像による超剛性定理および固定点定理へのアプローチ Invited Reviewed Open Access

井関裕靖、納谷信

数学 Vol. 158 page： 239-262 2006

*Combinatorial harmonic maps and discrete-group actions on Hadamard spaces Reviewed

Shin Nayatani, Izeki Hiroyasu

Geometriae Dedicata Vol. 114 page： 147-188 2005

組合せ調和写像と超剛性 --- SINGULAR TARGET の場合 Open Access

納谷信、井関裕靖

数理解析研究所講究録 Vol. 1329 page： 1-7 2003

組合せ調和写像と超剛性 Open Access

納谷信、井関裕靖

数理解析研究所講究録 Vol. 1270 page： 182-194 2002

Quaternionic analogue of CR geometry

Shin Nayatani, Hiroyuki Kamada

Séminaire de Théorie Spectrale et Géométrie Vol. 19 page： 41-52 2001

*Discrete groups of complex hyperbolic isometries and pseudo-Hermitian structures Invited Reviewed

Analysis and Geometry in Several Complex Variables, Proceedings of the 40th Taniguchi Symposium, Birkh(]E88D2[)user page： 209-237 1999

Canonical metric on the domain of discontinuty of a Kleinian group(共著)

S(]E85C2[)minaire de Th(]E85C2[)orie Spectrale et G(]E85C2[)om(]E85C2[)trie Vol. 16 page： 9-32 1998

*Patterson-Sullivan measure and conformally flat metrics Reviewed

Mathematische Zeitschrift Vol. 225 page： 115-131 1997

*Self-dual manifolds with positive Ricci curvature(共著) Reviewed

Mathematische Zeitschrift Vol. 224 page： 49-63 1997

Morse indices of Yang-Mills connections over the unit sphere (共著)

Composition Mathematica Vol. 98 page： 177-192 1995

*Morse index and Gauss maps of complete minimal surfaces in Euclidean 3-space Reviewed

Commentarii Mathematici Helvetici ( 68 ) page： 511-537 1993

Spectrum of the Schr(]E88D8[)dinger operator on a complete manifold (共著)

Journal of Functional Analysis ( 112 ) page： 459-479 1993

Complete conformal metrics with prescribed scalar curvature on subdomains of a compact manifold (共著)

Nagoya Mathematical Journal ( 132 ) page： 155-173 1993

Kleinian groups and conformally flat metrics

Geometry and Global Analysis, Report of the First MSJ International Research Institute page： 341-349 1993

Morse index of complete minimal surfaces

THE PROBLEM OF PLATEAU ed. Th. M. Rassias, World Scientific, Singapore page： 181-189 1992

On the Morse index of complete minimal surfaces in Euclidean space

Osaka Journal of Mathematics ( 27 ) page： 441-451 1990

Lower bounds for the Morse index of complete minimal surfaces in Euclidean 3-space

Osaka Journal of Mathematics ( 27 ) page： 453-464 1990

On the volume of positively curved Kaehler manifolds Reviewed

Osaka Journal of Mathematics ( 25 ) page： 223-231 1988

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Papers - NAYATANI, Shin