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

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 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

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

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AU - Ponnusamy, Saminathan

AU - Rasila, Antti

AU - Wang, Xian Tao

N1 - Publisher Copyright: © 2016, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg. Copyright: Copyright 2016 Elsevier B.V., All rights reserved.

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

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Keywords

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