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

Shao Lin Chen; Saminathan Ponnusamy; Antti Rasila; Xian Tao Wang

doi:10.1007/s10114-016-4259-3

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 journal › Article › peer-review

14 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 language	English
Pages (from-to)	297-308
Number of pages	12
Journal	Acta Mathematica Sinica, English Series
Volume	32
Issue number	3
DOIs	https://doi.org/10.1007/s10114-016-4259-3
State	Published - 1 Mar 2016
Externally published	Yes

Keywords

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

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10.1007/s10114-016-4259-3

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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.",

keywords = "Harmonic mapping, John constant, Schwarz–Pick lemma, a-close-to-convex function, linearly connected domain, univalency",

author = "Chen, {Shao Lin} and Saminathan Ponnusamy and Antti Rasila and Wang, {Xian Tao}",

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AU - Ponnusamy, Saminathan

AU - Rasila, Antti

AU - Wang, Xian Tao

PY - 2016/3/1

Y1 - 2016/3/1

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KW - John constant

KW - Schwarz–Pick lemma

KW - a-close-to-convex function

KW - linearly connected domain

KW - univalency

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

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