Lengths, areas and Lipschitz-type spaces of planar harmonic mappings
Shaolin Chen, Saminathan Ponnusamy, Antti Rasila
TL;DR
This paper investigates harmonic mappings in the plane, establishing a three circles theorem related to harmonic area, providing bounds on length and area distortion for harmonic quasiconformal maps, and exploring Lipschitz-type spaces.
Contribution
It introduces a three circles theorem for harmonic area, bounds distortion in harmonic quasiconformal mappings, and studies Lipschitz-type spaces for harmonic mappings.
Findings
Established a three circles theorem involving harmonic area.
Provided bounds for length and area distortion in harmonic quasiconformal mappings.
Analyzed properties of Lipschitz-type spaces in harmonic mappings.
Abstract
In this paper, we establish a three circles type theorem, involving the harmonic area function, for harmonic mappings. Also, we give bounds for length and area distortion for harmonic quasiconformal mappings. Finally, we will study certain Lipschitz-type spaces on harmonic mappings.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Algebraic and Geometric Analysis