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 journalArticleScientificpeer-review

13 Citations (Scopus)

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
Publication statusPublished - Mar 2016
MoE publication typeA1 Journal article-refereed

Keywords

  • Harmonic mapping
  • linearly connected domain
  • Schwarz-Pick lemma
  • alpha-close-to-convex function
  • John constant
  • univalency
  • JOHN CONSTANT

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