Bi-lipschitz property and distortion theorems for planar harmonic mappings with M-linearly connected holomorphic part

Jie Huang, Jian Feng Zhu

Research output: Contribution to journalArticlepeer-review

Abstract

Let f = h + g be a harmonic mapping of the unit disk D with the holomorphic part h satisfying that h is injective and h(D) is an M-linearly connected domain. In this paper, we obtain the sufficient and necessary conditions for f to be bi-Lipschitz, which is in particular, quasiconformal. Moreover, some distortion theorems are also obtained.

Original languageEnglish
Pages (from-to)1419-1431
Number of pages13
JournalBulletin of the Korean Mathematical Society
Volume55
Issue number5
DOIs
StatePublished - 2018
Externally publishedYes

Keywords

  • Bi-lipschitz mapping
  • Harmonic mapping
  • M-linearly connected domain
  • Quasiconformal mapping

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