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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Univalence criteria and quasiconformal extensions
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by J. M. Anderson and A. Hinkkanen PDF
Trans. Amer. Math. Soc. 324 (1991), 823-842 Request permission

Abstract:

Let $f$ be a locally univalent meromorphic function in the unit disk $\Delta$. Recently, Epstein obtained a differential geometric proof for the fact that if $f$ satisfies an inequality involving a suitable real-valued function $\sigma$, then $f$ is univalent in $\Delta$ and has a quasiconformal extension to the sphere. We give a more classical proof for this result by means of an explicit quasiconformal extension, and obtain generalizations of the result under suitable conditions even if $\sigma$ is allowed to be complex-valued and $\Delta$ is replaced by a quasidisk.
References
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 324 (1991), 823-842
  • MSC: Primary 30C55; Secondary 30C62
  • DOI: https://doi.org/10.1090/S0002-9947-1991-0994162-4
  • MathSciNet review: 994162