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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Holomorphic motions and Teichmüller spaces
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by C. J. Earle, I. Kra and S. L. Krushkal′ PDF
Trans. Amer. Math. Soc. 343 (1994), 927-948 Request permission

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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Additional Information
  • © Copyright 1994 American Mathematical Society
  • 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