On extendibility of a map induced by Bers isomorphism

Abstract

Let $S$ be a closed Riemann surface of genus $g(\geqq 2)$ and set $\dot{S}=S\setminus \{{\hat{z}}_0\}$. Then we have the composed map $\phi \circ r$ of a map $r:T(S)\times U\to F(S)$ and the Bers isomorphism $\phi :F(S)\to T(\dot{S})$, where $F(S)$ is the Bers fiber space of $S$, $T(X)$ is the Teichmüller space of $X$ and $U$ is the upper half-plane. The purpose of this paper is to show the map $\phi \circ r:T(S)\times U\to T(\dot{S})$. has a continuous extension to some subset of the boundary $T(S)\times \partial U$.

arXiv commentThis paper is accepted to Proceedings of AMS. This file is the final version