On extendibility of a map induced by the Bers isomorphism

Miyachi, Hideki; Nogi, Toshihiro

doi:10.1090/S0002-9939-2014-12140-X

On extendibility of a map induced by the Bers isomorphism
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by Hideki Miyachi and Toshihiro Nogi PDF

Proc. Amer. Math. Soc. 142 (2014), 4181-4189 Request permission

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 $\varphi \circ r$ of a map $r: T(S) \times U \rightarrow F(S)$ and the Bers isomorphism $\varphi : F(S) \rightarrow T(\dot {S})$, 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 that the map $\varphi \circ r:T(S)\times U \rightarrow T(\dot {S})$ has a continuous extension to some subset of the boundary $T(S) \times \partial U$.

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