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

Authors

Shao Lin Chen, Hengyang Normal University
Saminathan Ponnusamy, Indian Statistical Institute Chennai
Antti Rasila, Aalto University
Xian Tao Wang, Shantou University

Article Type

Research Article

Publication Title

Acta Mathematica Sinica, English Series

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.

First Page

297

Last Page

308

DOI

10.1007/s10114-016-4259-3

Publication Date

3-1-2016

Recommended Citation

Chen, Shao Lin; Ponnusamy, Saminathan; Rasila, Antti; and Wang, Xian Tao, "Linear connectivity, Schwarz–Pick lemma and univalency criteria for planar harmonic mapping" (2016). Journal Articles. 4276.
https://digitalcommons.isical.ac.in/journal-articles/4276