依赖参数的无穷小Strebel点

The Infinitesimal Strebel Points Depending on Parameters

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.