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Holomorphic motions and Teichmüller spaces


Authors: C. J. Earle, I. Kra and S. L. KrushkalЬ
Journal: Trans. Amer. Math. Soc. 343 (1994), 927-948
MSC: Primary 32G15; Secondary 30F60
DOI: https://doi.org/10.1090/S0002-9947-1994-1214783-6
MathSciNet review: 1214783
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Abstract: We prove an equivariant form of Slodkowski's theorem that every holomorphic motion of a subset of the extended complex plane $ \hat{\mathbb{C}}$ extends to a holomorphic motion of $ \widehat{\mathbb{C}}$. As a consequence we prove that every holomorphic map of the unit disc into Teichmüller space lifts to a holomorphic map into the space of Beltrami forms. We use this lifting theorem to study the Teichmüller metric.


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DOI: https://doi.org/10.1090/S0002-9947-1994-1214783-6
Article copyright: © Copyright 1994 American Mathematical Society

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