Criteria for univalence and quasiconformal extension of harmonic mappings in terms of the Schwarzian derivative

Rodrigo Hernández, María J. Martín

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We prove that if the Schwarzian norm of a given complex-valued locally univalent harmonic mapping f in the unit disk is small enough, then f is, indeed, globally univalent in the unit disk and can be extended to a quasiconformal mapping in the extended complex plane.

Original languageEnglish
Pages (from-to)53-59
Number of pages7
JournalArchiv der Mathematik
Volume104
Issue number1
DOIs
StatePublished - Jan 2014

Keywords

  • Harmonic mapping
  • Quasiconformal extension
  • Schwarzian derivative
  • Univalence criterion

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