Teichmuller spaces of symmetric structures and the rigidity and fixed-point problems of quasiconformal mapping class groups

对称结构的Teichmuller空间与拟共形映射类群的刚性和不动点问题

• 批准号: 20340030
• 负责人: MATSUZAKI Katsuhiko
• 金额: $ 10.82万
• 依托单位: Waseda University (2010-2012)Okayama University (2008-2009)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20340030/
• 关键词: 擬対称写像; 擬等角写像; メビウス変換群; 複素解析; 双曲幾何; 幾何学的群論; タイヒミュラー空間; リーマン面; フックス群; 写像類群; 双曲計量; フツクス群; モジュライ空間; クライン群

We define various classes for self-homeomorphisms of the unit circle from a viewpoint of their quasiconformal extension, and study the parameter spaces of those families, which are regarded as Teichmuller spaces. In particular, for the Teichmuller space of symmetric homeomorphisms, we consider conditions for a group acting on this space to have a fixed point in it. As an application, we give a condition for a group of diffeomorphisms to be conjugate to the canonical group action of the circle (Mobius transformations) as well as a condition for the deformation of such a group to be trivial (that is, to have rigidity).

从单位圆自同胚的拟共形扩展出发，定义了单位圆自同胚的各种类，研究了这些族的参数空间，并将其视为Teichmuller空间。特别地，对于对称同胚的Teichmuller空间，我们考虑了作用于该空间的群在该空间中有不动点的条件。作为应用，我们给出了一群微分同胚与圆的正则群作用（Mobius变换）共轭的条件，以及这群微分同胚的变形平凡（即具有刚性）的条件。

项目成果

Symmetric groups that are not the symmetric conjugates of Fuchsian groups, Geometric Function Theory and Geometry

不是 Fuchsian 群对称共轭的对称群、几何函数理论和几何

• 发表时间: 2008
• 作者: Yoshida;T.;Yoshitsugu Takei;A.Suzuki;K. Matsuzaki
• 通讯作者: K. Matsuzaki

Petersson series vanishes at infinity, Quasiconformal mappings, Riemann surfaces, and Teichmuller spaces

Petersson 级数消失于无穷远、拟共形映射、黎曼曲面和 Teichmuller 空间

• 发表时间: 2012
• 期刊: Contemporary Math
• 作者: 木村恵二;竹広真一;山田道夫;山田道夫;K. Matsuzaki
• 通讯作者: K. Matsuzaki

Polycyclic quasiconformal mapping class subgroups

多环拟共形映射类子群

• 发表时间: 2011
• 期刊: Pacific J. Math
• 作者: T. Kawai;T. Koike and Y. Takei;H. Nagai;H.Maehara;K. Matsuzaki
• 通讯作者: K. Matsuzaki

Topics in Finite or Infinite Dimensional Complex Analysis

有限或无限维复分析主题

• 发表时间: 2013
• 作者: K. Matsuzaki;K. Matsuzaki;K. Matsuzaki;Katsuhiko Matsuzaki;Katsuhiko Matsuzaki;E. Fujikawa and K. Matsuzaki;K. Matsuzaki and Y. Yabuki;K. Matsuzaki;K. Matsuzaki;松崎克彦;松崎克彦;Katsuhiko Matsuzaki;Katsuhiko Matsuzaki;Katsuhiko Matsuzaki;K. Matsuzaki;K. Matsuzaki;K. Matsuzaki;K. Matsuzaki;松崎克彦;K. Matsuzaki;松崎克彦;Katsuhiko Matsuzaki;Katsuhiko Matsuzaki;松崎克彦;Katsuhiko Matsuzaki;K. Matsuzaki and T. Sugawa
• 通讯作者: K. Matsuzaki and T. Sugawa

Rigidity of groups of circle diffeomorphisms and teichmüller spaces

• DOI: 10.1007/s11854-020-0095-6
• 发表时间: 2020-03
• 期刊: Journal d'Analyse Mathématique
• 作者: Katsuhiko Matsuzaki