Univalent harmonic mappings and linearly connected domains

M. Chuaqui, R. Hernández

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

Abstract

We investigate the relationship between the univalence of f and of h in the decomposition f = h + over(g, -) of a sense-preserving harmonic mapping defined in the unit disk D ⊂ C. Among other results, we determine the holomorphic univalent maps h for which there exists c > 0 such that every harmonic mapping of the form f = h + over(g, -) with | g | < c | h | is univalent. The notion of a linearly connected domain appears in our study in a relevant way.

Original languageEnglish
Pages (from-to)1189-1194
Number of pages6
JournalJournal of Mathematical Analysis and Applications
Volume332
Issue number2
DOIs
StatePublished - 15 Aug 2007

Keywords

  • Harmonic mapping
  • Linearly connected domain
  • Second complex dilatation
  • Univalent

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