Teichmuller Spaces and Mapping Class Groups

Teichmuller 空间和映射类组

• 批准号: 10440059
• 负责人: IMAYOSHI Yoichi
• 金额: $ 2.43万
• 依托单位: Osaka City University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B).
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-10440059/
• 关键词: Teichmuller space; Riemann sueface; Kleinian group; quasi-conformal mapping; mapping class group; Teichmuller modular group; holomorphic mapping; harmonic mapping; 正則族; モデュライ空間; 複素多様体; 正則2次微分

Mainly we studied the following three themes :1. By using Bers-Thurston classification of elements of mapping class groups, we determined types of elements of monodormy groups of holomorphic families of Riemann surfaces, especially induced by Kodaira surfaces.2. We gived a condition for harmonic maps between compact hyperbolic Riemann surfaces so that they are holomorphi or anti-holomorphic.3. We gave an estimate of the number of non-constant holomorphic maps between compact hyperbolic Riemann surfaces by topological data.

我们主要研究了以下三个主题：1。通过使用映射类组的元素元素分类，我们确定了riemann表面的全态家族的单型群体的元素类型，尤其是由Kodaira表面诱导的元素。2。我们为紧凑的双曲riemann表面之间的谐波图提供了一个条件，以便它们是Holomorphi或抗旋晶。3。我们通过拓扑数据对紧凑型双曲riemann表面之间的非恒定溶性图的数量进行了估计。

项目成果

J.Noguchi: "On holomorphic curves in semi-Abelian varieties"Math.Z.. 228. 713-721 (1998)

J.Noguchi：“论半阿贝尔簇的全纯曲线”Math.Z.. 228. 713-721 (1998)

Atsushi Kasue: "Riemannian submersians and isoperimetric in equalities" Geometriae Dedicata. 70. 27-47 (1998)

Atsushi Kasue：“黎曼潜水器和等周等式”Geometriae Dedicata。

Atsushi Kasue: "Convergence of Riemannian manifolds and Laplace operators; I"Ann.Institut Fourier. (発表予定).

Atsushi Kasue：“黎曼流形和拉普拉斯算子的收敛；I”Ann.Institut Fourier（即将提交）。

A.Kasue: "Convergence of Riemannian manifolds, Laplace operators and energy forms"Proc. of the fifth Pacific Rim Gemetric Conference, Tohoku Mathematical Publications. (to appear).

A.Kasue：“黎曼流形、拉普拉斯算子和能量形式的收敛性”Proc。

Masahiko Taniguchi: "A condition of quasi conformal extendofility"Proc.Japan Acad.Ser A.Math.Sci.. 75. 58-60 (1999)

Masahiko Taniguchi：“准保形扩展的条件”Proc.Japan Acad.Ser A.Math.Sci.. 75. 58-60 (1999)