摘要
本文主要讨论万有Ｔｅｉｃｈｍｔｉｌｌｅｒ空间中的测地线问题，并给出了一些测地线不唯一的判断准则．特别地，证明了如下定理：设ｆ是单位圆△到自身上的极值拟共形映射，μ是它的复特征，如果存在常数ｋ．＜｜｜μ｜｜＿∞，使集合｛ｚ∈△：｜μ（Ｚ）｜≤ｋ｝有内点，则在万有Ｔｅｉｃｈｍｕｌｌｅｒ空间中，原点［０］与［μ］之间存在无穷多条测地线．
The purpose of the paper is to discuss the geodesic problem in the universal Te-ichmtiller space. Some criteria of non-uniqueness of geodesics are given. Especially,the followingtheorem is proved:Let f be an extremal quasiconformal mapping of the unit disk △ onto itself,and μ its complex dilatation. Suppose that there exists a constant such that the sethas an interior point,then there exist infinitely many geodesics joining thepoint [0]and[μ].
出处
《数学进展》
CSCD
北大核心
1995年第3期237-243,共7页
Advances in Mathematics（China）
关键词
T空间
拟共形映射
测地线
极值映射
Teichmuller space
extremal Beltrami differential
extremal quasiconformalmapping
geodesic
