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arXiv · 2208.03280

Two-point distortion theorems for harmonic mappings

Víctor Bravo·Rodrigo Hernández·Osvaldo Venegas
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Abstract

We establish two-point distortion theorems for sense-preserving planar harmonic mappings $f=h+\overline{g}$ which satisfies the univalence criteria in the unit disc such that, Becker's and Nehari`s harmonic version. In addition, we find the sharp two-point distortion theorem when $h$ is a convex function, and normalized mappings such that $h(\D)$ is a $c$-linearly connected domain. To do this, we use the order of this family.

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Víctor Bravo, Rodrigo Hernández, Osvaldo Venegas. 2022-08-05. Two-point distortion theorems for harmonic mappings. https://arxiv.org/abs/2208.03280

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