Katsuhiko Matsuzaki

J-GLOBAL         Last updated: Sep 6, 2019 at 23:40
Katsuhiko Matsuzaki
Waseda University
Faculty of Education and Integrated Arts and Sciences School of Education
Job title
Research funding number

Research Interests


Research Areas



Faculty of Science, Kyoto University
Graduate School, Division of Natural Science, Kyoto University

Published Papers

Matsuzaki Katsuhiko
Katsuhiko Matsuzaki
Groups, Geometry, and Dynamics   12(1) 1-64   Jan 2018   [Refereed]
© European Mathematical Society. We investigate the dynamics of the Teichmüller modular group on the Teichmüller space of a Riemann surface of infinite topological type. Since the modular group does not necessarily act discontinuously, the quotien...
Matsuzaki Katsuhiko
Matsuzaki, Katsuhiko; Rodríguez, José M.
Mathematische Nachrichten   290(7) 1097-1112   May 2017   [Refereed]
© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimWe consider a planar Riemann surface R made of a non-compact simply connected plane domain from which an infinite discrete set of points is removed. We give several conditions for the collars of the...
Jaerisch, Johannes; Matsuzaki, Katsuhiko
Proceedings of the American Mathematical Society   145(10) 4141-4149   Jan 2017   [Refereed]
© 2017 American Mathematical Society. We give a sufficient condition for a sequence of normal subgroups of a free group to have the property that both their growths tend to the upper bound and their cogrowths tend to the lower bound. The condition...
Matsuzaki, Katsuhiko; Yanagishita, Masahiro
Filomat   31(1) 85-90   Jan 2017   [Refereed]
© 2017, University of Nis. All rights reserved. We first remark that the complex dilatation of a quasiconformal homeomorphism of a hyperbolic Riemann surface R obtained by the barycentric extension due to Douady-Earle vanishes at any cusp of R. Th...
Matsuzaki, Katsuhiko
Journal of the Mathematical Society of Japan   69(1) 263-292   Jan 2017   [Refereed]
©2017 The Mathematical Society of Japan. For a regularly locally compact topological space X of T 0 separation axiom but not necessarily Hausdorff, we consider a map σ from X to the hyperspace C(X) of all closed subsets of X by taking the closure ...
Katsuhiko Matsuzaki
Annales Academiae Scientiarum Fennicae Mathematica   42 535-550   Jan 2017
© 2017 Annales Academiæ Scientiarum Fennicæ Mathematica. We introduce the quasisymmetric deformation space of a Fuchsian group Γ within the group of symmetric self-homeomorphisms of the circle, and define this as the Teichmüller space AT (Γ) of Γ-...
Matsuzaki Katsuhiko
Matsuzaki, Katsuhiko
Topology and its Applications   196 684-695   Dec 2015   [Refereed]
© 2015 Elsevier B.V. We say that a complete metric space X has the fixed point property if every group of isometric automorphisms of X with a bounded orbit has a fixed point in X. We prove that if X is uniformly convex then the family of admissibl...
Falk, Kurt; Matsuzaki, Katsuhiko
Conformal Geometry and Dynamics   19(8) 159-196   Jan 2015   [Refereed]
© 2015 American Mathematical Society. In this paper we study the relationship between three numerical invariants associated to a Kleinian group, namely the critical exponent, the Hausdorff dimension of the limit set and the convex core entropy, wh...
Matsuzaki, Katsuhiko
Computational Methods and Function Theory   14(2-3) 487-503   Jan 2014   [Refereed]
© 2014, Springer-Verlag Berlin Heidelberg. Using the correspondence between the quasisymmetric quotient and the variation of the cross-ratio for a quasisymmetric automorphism (Formula presented.) of the unit circle, we establish a certain integrab...
Matsuzaki, Katsuhiko
Complex Variables and Elliptic Equations   58(7) 923-932   Jul 2013   [Refereed]
We introduce a certain extremal problem for quasiconformal automorphisms of annuli and give upper and lower estimates for the minimal value of their maximal dilatations. © 2013 Copyright Taylor and Francis Group, LLC.
Fujikawa, Ege; Matsuzaki, Katsuhiko
Transactions of the American Mathematical Society   365(6) 3309-3327   Apr 2013   [Refereed]
Under a certain geometric assumption on a hyperbolic Riemann surface, we prove an asymptotic version of the fixed point theorem for the Teichm̈uller modular group, which asserts that every finite subgroup of the asymptotic Teichm̈uller modular gro...
Matsuzaki Katsuhiko, Yabuki Yasuhiro
IN THE TRADITION OF AHLFORS-BERS, VI   590 125-136   2013   [Refereed]
Bonfert-Taylor, Petra; Matsuzaki, Katsuhiko; Taylor, Edward C.
Journal of Geometric Analysis   22(2) 455-470   Apr 2012   [Refereed]
The exponent of convergence of a non-elementary discrete group of hyperbolic isometries measures the Hausdorff dimension of the conical limit set. In passing to a non-trivial regular cover the resulting limit sets are point-wise equal though the e...
Matsuzaki Katsuhiko
Matsuzaki, Katsuhiko
Pacific Journal of Mathematics   251(2) 361-374   Jun 2011   [Refereed]
For a subgroup of the quasiconformal mapping class group of a Riemann surface in general, we give an algebraic condition which guarantees its discreteness in the compact-open topology. Then we apply this result to its action on the Teichmüller spa...
Fujikawa, Ege; Matsuzaki, Katsuhiko
American Journal of Mathematics   133(3) 637-675   Jun 2011   [Refereed]
The stable quasiconformal mapping class group is a group of quasiconformal mapping classes of a Riemann surface that are homotopic to the identity outside some topologically finite subsurface. Its analytic counterpart is a group of mapping classes...
Matsuzaki, Katsuhiko; Rodríguez, José M.
Acta Mathematica Sinica, English Series   27(1) 29-44   Jan 2011   [Refereed]
The main aim of this paper is to study whether the Gromov hyperbolicity is preserved under some transformations on Riemann surfaces (with their Poincaré metrics). We prove that quasiconformal maps between Riemann surfaces preserve hyperbolicity; h...
Falk, Kurt; Matsuzaki, Katsuhiko; Stratmann, Bernd O.
Conformal Geometry and Dynamics   3(8) 116-150   Jun 2010
In this paper we address questions of continuity and atomicity of conformal ending measures for arbitrary non-elementary Kleinian groups. We give sufficient conditions under which such ending measures are purely atomic. Moreover, we will show that...
Symmetric groups that are not the symmetric conjugates of Fuchsian groups
Matsuzaki Katsuhiko
IN THE TRADITION OF AHLFORS-BERS, V   510 239-247   2010   [Refereed]
Katsuhiko Matsuzaki, Yasuhiro Yabuki
Ergodic Theory and Dynamical Systems   29 657-665   Apr 2009   [Refereed]
A Kleinian group (a discrete subgroup of conformal automorphisms of the unit ball) G is said to have proper conjugation if it contains the conjugate αGα-1 by some conformal automorphism α as a proper subgroup in it. We show that a Kleinian group o...
Katsuhiko Matsuzaki
Illinois Journal of Mathematics   52(4) 1249-1258   Dec 2008   [Refereed]
We characterize convergence and divergence types for Fuchsian groups in terms of the critical exponent of convergence and modified functions of the Poincaré series for certain subgroups associated with ends of the quotient Riemann surfaces. As an ...
Fujikawa Ege, Matsuzaki Katsuhiko, Taniguchi Masahiko
MATHEMATISCHE ZEITSCHRIFT   260(4) 865-888   Dec 2008   [Refereed]
Matsuzaki Katsuhiko, Yabuki Yasuhiro
GEOMETRIAE DEDICATA   135(1) 147-155   Aug 2008   [Refereed]
Matsuzaki Katsuhiko
JOURNAL D' ANALYSE MATHEMATIQUE   102 1-28   Aug 2007   [Refereed]
Matsuzaki, Katsuhiko
Proceedings of the American Mathematical Society   135(8) 2573-2579   Aug 2007   [Refereed]
For an analytically infinite Riemann surface R, the quasiconformal mapping class group MCG(R) always acts faithfully on the ordinary Teichmüller space T(R). However in this paper, an example of R is constructed for which MCG(R) acts trivially on i...
Non-stationary and discontinuous quasiconformal mapping class groups
Fujikawa Ege, Matsuzaki Katsuhiko
OSAKA JOURNAL OF MATHEMATICS   44(1) 173-185   Mar 2007   [Refereed]
The interior of discrete projective structures in the Bers fiber
Matsuzaki Katsuhiko
A classification of the modular transformations of infinite dimensional Teichmuller spaces
Matsuzaki Katsuhiko
In the Tradition of Ahlfors-Bers, IV   432 167-177   2007   [Refereed]
Fujikawa, Ege; Matsuzaki, Katsuhiko
Indiana University Mathematics Journal   55(3) 975-997   Aug 2006   [Refereed]
We study the action of isometries on metric spaces. In particular, we consider the recurrent set of the bilateral shift operator on the Banach space L ∞ (ℤ), and prove that the set of periodic points is not dense in the recurrent set. Then we app...
Matsuzaki, Katsuhiko
Transactions of the American Mathematical Society   357(8) 3119-3131   Aug 2005
We construct an example of a Riemann surface of infinite topological type for which the Teichmüller modular group consists of only a countable number of elements. We also consider distinguished properties which the Teichmüller space of this Rieman...
Matsuzaki, Katsuhiko
Kodai Mathematical Journal   28(2) 292-300   Jan 2005
The critical exponents of conservative Fuchsian groups are bounded from below by 1/2. It is proved in this note that this result is sharp by giving a sequence of conservative Fuchsian groups whose critical exponents converge to 1/2. The proof is c...
Katsuhiko Matsuzaki
Israel Journal of Mathematics   140 113-123   Jan 2004
We prove that if the Bers embeddings of the Teichmüller spaces of infinitely generated Fuchsian groups are coincident, then these Fuchsian groups are the same.
Matsuzaki, Katsuhiko
Kodai Mathematical Journal   26(3) 279-287   Jan 2003
Simply connected domains on a hyperbolic surface
Katsuhiko Matsuzaki
New Zealand Journal of Mathematics   31 159-164   2002   [Refereed]
Conservative action of Kleinian groups with respect to the Patterson-Sullivan measure
Katsuhiko Matsuzaki
Computational Methods and Function Theory   2 469-479   2002   [Refereed]
Matsuzaki, Katsuhiko; Matsuzaki, Katsuhiko
Mathematical Proceedings of the Cambridge Philosophical Society   128(1) 123-139   Jan 2000
In this paper we investigate the Hausdorff dimension of the limit set of an infinitely generated discrete subgroup of hyperbolic isometries and obtain conditions for the limit set to have full dimension. © 2000 Cambridge Philosophical Society.
Katsuhiko Matsuzaki
Michigan Mathematical Journal   44 21-36   Jan 1997
Conformal conjugation of Fuchsian groups from the first kind to the second kind
Matsuzaki, Katsuhiko; Shiga, Hiroshige
Journal fur die Reine und Angewandte Mathematik   (476) 191-200   Dec 1996
Matsuzaki, Katsuhiko
Duke Mathematical Journal   78(2) 413-425   Jan 1995   [Refereed]
The conservative-dissipative dichotomy for geometric covers of Riemann surfaces
Katsuhiko Matsuzaki
Revue Roumaine de Mathématiques Pures et Appliquées   40 77-80   1995   [Refereed]
Teichmüller spaces with variable bases in the universal Teichmüller space
Katsuhiko Matsuzaki
Annales Academiae Scientiarum Fennicae Mathematica   20 27-36   1995   [Refereed]
Matsuzaki K, Velling J.A.
Osaka Journal of Mathematics   31(1) 165-175   1994   [Refereed]
Ergodic properties of discrete groups; inheritance to normal subgroups and invariance under quasiconformal deformations
Katsuhiko Matsuzaki
Journal of Mathematics of Kyoto University   33 205-226   1993   [Refereed]
Simply connected invariant domains of Kleinian groups not in the closures of Teichmüller spaces
Katsuhiko Matsuzaki
Complex Variables   22 93-100   1993   [Refereed]
Matsuzaki, Katsuhiko
Tohoku Mathematical Journal   43(3) 327-336   Jan 1991   [Refereed]
Velling J.A, Matsuzaki K.
Ergodic Theory and Dynamical Systems   11(3) 577-582   1991   [Refereed]
A characterization of extended Schottky type groups with a remark to Ahlfors' conjecture
Katsuhiko Matsuzaki
Journal of Mathematics of Kyoto University   31 259-264   1991   [Refereed]
Matsuzaki K.
Kodai Mathematical Journal   13(3) 377-385   1990   [Refereed]


RIMS Kokyuroku Bessatsu   17 21-36   Jun 2010
Fujikawa Ege, Matsuzaki Katsuhiko, Taniguchi Masahiko
RIMS Kokyuroku   1494 44-48   May 2006
Matsuzaki Katsuhiko
RIMS Kokyuroku   1329 58-61   Jun 2003
Matsuzaki Katsuhiko
RIMS Kokyuroku   1163 42-45   Jul 2000
Matsuzaki Katsuhiko
RIMS Kokyuroku   1065 106-107   Oct 1998
松崎 克彦
Science bulletin of Josai University, Special Issue   4 25-28   1998
NLA97 : Complex Dynamical Systems : The Second Symposium on Non-Linear Analysis and its Applications. / Edited by KIYOKO NISHIZAWA. 29-31 May 1997. The Conference Hall, MIZUTA Memorial Library Josai University.
Matsuzaki Katsuhiko
RIMS Kokyuroku   1022 87-92   Dec 1997
RIMS Kokyuroku   967 117-120   Oct 1996
数理解析研究所講究録   882 51-56   Aug 1994

Books etc

Hyperbolic Manifolds and Kleinian Groups
Katsuhiko Matsuzaki and Masahiko Taniguchi
Oxford University Press   Apr 1998   ISBN:978-0-19-850062-9

Research Grants & Projects

Teichmuller spaces of symmetric structures and the rigidity and fixed-point problems of quasiconformal mapping class groups
Project Year: Apr 2008 - Mar 2013
Researches on quasiconformal groups and the modular group of the universal Teichmuller space
Project Year: Apr 2004 - Mar 2008
Dynamics of modular groups on infinite dimensional Teichmuller spaces
Project Year: Apr 2002 - Mar 2004
Deformation theory of Kleinian groups
Project Year: Apr 1997 - Mar 1999
Research on deformations of real and complex manifolds and variations of invariants
New development of geometric function theory focused on conformal invariants
Analysis of Complex Dynamics
Potential theory in a domain with fractal boundary
Study of various problems in mathematical physics