Linear connectivity, Schwarz–Pick lemma and univalency criteria for planar harmonic mapping

Shao Lin Chen, Saminathan Ponnusamy, Antti Rasila, Xian Tao Wang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

In this paper, we first establish a Schwarz–Pick lemma for higher-order derivatives of planar harmonic mappings, and apply it to obtain univalency criteria. Then we discuss distortion theorems, Lipschitz continuity and univalency of planar harmonic mappings defined in the unit disk with linearly connected images.

Original languageEnglish
Pages (from-to)297-308
Number of pages12
JournalActa Mathematica Sinica, English Series
Volume32
Issue number3
DOIs
StatePublished - 1 Mar 2016
Externally publishedYes

Keywords

  • a-close-to-convex function
  • Harmonic mapping
  • John constant
  • linearly connected domain
  • Schwarz–Pick lemma
  • univalency

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