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Holomorphic mappings into Teichmüller spaces


Author: Harumi Tanigawa
Journal: Proc. Amer. Math. Soc. 117 (1993), 71-78
MSC: Primary 32G15; Secondary 30F10, 30F60
DOI: https://doi.org/10.1090/S0002-9939-1993-1113649-4
MathSciNet review: 1113649
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Abstract: Let $ T(F)$ be the Teichmüller space of a finitely generated Fuchsian group $ F$ of the first kind. We shall show that there exists no nontrivial family of holomorphic proper mappings of the unit disc into $ T(F)$ with a complex analytic parameter. Using this result, we shall investigate a family of quasi-conformal mappings with a complex analytic parameter whose Beltrami differentials vanish on a fixed set of positive area.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1113649-4
Article copyright: © Copyright 1993 American Mathematical Society

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