Teichmuller空间的星形结构问题  

On the Problem of Starlikeness of Teichmuller Spaces

作　　者：沈玉良[1] 

机构地区：[1]北京大学数学系

出　　处：《数学学报（中文版）》1995年第4期462-466,共5页Acta Mathematica Sinica：Chinese Series

摘　　要：对于任一保持单位圆盘Δ及其外部Δ的Ｆｕｃｈｓ群Γ，利用Ｂｅｒｓ嵌入，Ｔｅｉｃｈｍｕｌｌｅｒ空间Ｔ（Γ）可看成是Δ上Γ的有界全纯二次微分Ｂ（Δ，Γ）中的一个有界区域，本文的目的是讨论Ｔｅｉｃｈｍｕｌｌｅｒ空间Ｔ（Γ）的星形问题。特别地，我们证明了：当Γ是第二类Ｆｕｃｈｓ群时，Ｔ（Γ）不是星形的．Let Γ be a Fuchsian group acting on the unit disk Δ. The Bers embedding repre-sents the Teichmuller space T(Γ)of Γ as a bounded domain in the space of bounded quadraticdifferentials for Γ. Our main result is: There exists a universal constant d_0>0 such that, for anygiven Fuchaian group Γ,suppose that there exists a hyperbolic disk in Δ of radius whichis precisely invariant under the trivial subgroup{1} of Γ, then T(Γ)is not starlike. Particullary,when Γ is a Fuchsian group of the second kind,T(Γ)is not starlike.

关 键 词：Bers嵌入 星形 T空间 Fuchs群 全纯函数 

分 类 号：O174.5[理学—数学]