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On extendibility of a map induced by the Bers isomorphism


Authors: Hideki Miyachi and Toshihiro Nogi
Journal: Proc. Amer. Math. Soc. 142 (2014), 4181-4189
MSC (2010): Primary 30F60, 32G15, 20F67
DOI: https://doi.org/10.1090/S0002-9939-2014-12140-X
Published electronically: August 1, 2014
MathSciNet review: 3266988
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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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Additional Information

Hideki Miyachi
Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Machi- kaneyama 1-1, Toyonaka, Osaka, 560-0043, Japan
Email: miyachi@math.sci.osaka-u.ac.jp

Toshihiro Nogi
Affiliation: Osaka City University Advanced Mathematical Institute, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
Email: toshihironogi8@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2014-12140-X
Received by editor(s): February 10, 2012
Received by editor(s) in revised form: June 13, 2012, and January 8, 2013
Published electronically: August 1, 2014
Additional Notes: The first author was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C), 21540177.
The second author was partially supported by the JSPS Institutional Program for Young Research Overseas Visits “Promoting international young researchers in mathematics and mathematical sciences led by OCAMI”
Communicated by: Michael Wolf
Article copyright: © Copyright 2014 American Mathematical Society