Teichmuller Spaces and Mapping Class Groups

主要研究了以下三个主题：1.利用Bers-Thurston对映射类群元素的分类，确定了全纯Riemann曲面族，特别是科代拉曲面族的单味群的元素类型.给出了紧致双曲Riemann曲面间调和映射是全纯或反全纯的条件。利用拓扑数据给出了紧致双曲Riemann曲面之间非常数全纯映射个数的估计。

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.