Remote Access Transactions of the American Mathematical Society
Green Open Access

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
MathSciNet review: 994162
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 30C55, 30C62

Retrieve articles in all journals with MSC: 30C55, 30C62

Additional Information

Article copyright: © Copyright 1991 American Mathematical Society