Kobayashi’s and Teichmuller’s Metrics and Bers Complex Manifold Structure on Circle Diffeomorphisms |
| |
作者姓名: | Yun Ping JIANG |
| |
作者单位: | Department of Mathematics;Department of Mathematics |
| |
基金项目: | This material is based upon work supported by the National Science Foundation. It is also partially supported by a collaboration grant from the Simons Foundation (Grant No. 523341) and PSC-CUNY awards and a grant from NSFC (Grant No. 11571122) |
| |
摘 要: | Given a modulus of continuity ω,we consider the Teichmuller space TC1+ω as the space of all orientation-preserving circle diffeomorphisms whose derivatives are ω-continuous functions modulo the space of Mobius transformations preserving the unit disk.We study several distortion properties for diffeomorphisms and quasisymmetric homeomorphisms.Using these distortion properties,we give the Bers complex manifold structure on the Teichm(u| ")ller space TC^1+H as the union of over all0 <α≤1,which turns out to be the largest space in the Teichmuller space of C1 orientation-preserving circle diffeomorphisms on which we can assign such a structure.Furthermore,we prove that with the Bers complex manifold structure on TC^1+H ,Kobayashi’s metric and Teichmuller’s metric coincide.
|
关 键 词: | Bers complex manifold STRUCTURE circle DIFFEOMORPHISM modulus of continuity quasisymmetric circle HOMEOMORPHISM Teichmuller space Kobayashi's METRIC Teichmuller's METRIC |
本文献已被 维普 SpringerLink 等数据库收录! |
| 点击此处可从《数学学报(英文版)》浏览原始摘要信息 |
| 点击此处可从《数学学报(英文版)》下载免费的PDF全文 |