Linear connectivity, Schwarz-Pick lemma and univalency criteria for planar harmonic mappings
Shaolin Chen, Saminathan Ponnusamy, Antti Rasila, Xiantao Wang
TL;DR
This paper extends the Schwarz-Pick lemma to higher orders and uses it to develop criteria for univalency of planar harmonic mappings, also exploring distortion, Lipschitz continuity, and linear connectivity of their images.
Contribution
It introduces higher-order Schwarz-Pick lemma applications and new univalency criteria for harmonic mappings with linearly connected images.
Findings
Established higher-order Schwarz-Pick lemma
Derived univalency criteria for harmonic mappings
Analyzed distortion and Lipschitz properties
Abstract
In this paper, we first establish the Schwarz-Pick lemma of higher-order and apply it to obtain a univalency criteria for planar harmonic mappings. Then we discuss distortion theorems, Lipschitz continuity and univalency of planar harmonic mappings defined in the unit disk with linearly connected images.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Algebraic and Geometric Analysis