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Transactions of the American Mathematical Society

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

 
 

 

Univalence criteria and quasiconformal extensions


Authors: J. M. Anderson and A. Hinkkanen
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
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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.


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Article copyright: © Copyright 1991 American Mathematical Society