Univalence criteria and quasiconformal extensions

J. M. Anderson, A. Hinkkanen

Research output: Contribution to journalArticlepeer-review

Abstract

Let f be a locally univalent meromorphic function in the unit disk Δ. Recently, Epstein obtained a differential geometric proof for the fact that if f satisfies an inequality involving a suitable real-valued function σ, then f is univalent in Δ 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 σ is allowed to be complex-valued and Δ is replaced by a quasidisk.

Original languageEnglish (US)
Pages (from-to)823-842
Number of pages20
JournalTransactions of the American Mathematical Society
Volume324
Issue number2
DOIs
StatePublished - Apr 1991

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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