Holomorphic mappings into Teichmüller spaces

Tanigawa, Harumi

doi:10.1090/S0002-9939-1993-1113649-4

Holomorphic mappings into Teichmüller spaces
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by Harumi Tanigawa

Proc. Amer. Math. Soc. 117 (1993), 71-78

DOI: https://doi.org/10.1090/S0002-9939-1993-1113649-4

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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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