依赖参数的无穷小Strebel点  

The Infinitesimal Strebel Points Depending on Parameters

作　　者：黄华鹰[1] HUANG Huaying(School of Mathematical Sciences,Anhui University,Hefei,Anhui,230601,P.R.China)

机构地区：[1]安徽大学数学科学学院,合肥安徽230601

出　　处：《数学进展》2022年第6期1145-1151,共7页Advances in Mathematics（China）

基　　金：Supported by NSFC(No.11771266)。

摘　　要：给定单位圆Δ内一个有界可测函数μ(z),且∥μ∥∞=k∈(0,1/3),本文考察μ_(t)(z)=tμ(z)的Teichmüller等价类[μ_(t)].我们找到了一族全纯依赖于复参数t的有界可测函数ν_(t)∈[μ_(t)],使得ν_(t)(z)的无穷小Teichmüller等价类[ν_(t)]B均是无穷小Strebel点,且使得t↦[ν_(t)]B是单位圆Δ到无穷小Teichmüller空间Z的全纯映射.Given a bounded measurable functionμ(z)on the unit diskΔ,with∥μ∥∞=k∈(0,1/3),for every t∈Δ,setμt(z)=tμ(z).Then there exists ν_(t)∈[μ_(t)],which is the Teichmüller equivalent class of μ_(t),such that the infinitesimal Teichmüller equivalent class[ν_(t)]B of ν_(t) is an infinitesimal Strebel point,moreover t↦νt is holomorphic and t↦[ν_(t)]B is also a holomorphic mapping fromΔto the infinitesimal Teichmüller space Z.

关 键 词：TEICHMÜLLER空间 拟共形映射 Strebel点 无穷小Strebel点 全纯运动 

分 类 号：O174.55[理学—数学]