Nehari‐type families of harmonic mappings

Hugo Arbeláez, Martin Chuaqui and Willy Sierra

Mathematische Nachrichten, 2020, vol. 293, issue 1, 39-51

Abstract: We introduce affine and linearly invariant families of locally injective harmonic mappings of the unit disk D. We derive sharp distortion theorems for the Jacobian that are used to establish a uniform modulus of continuity for the quasiconformal mappings in each class. Finally, we find a converse of a recent theorem of Chen and Ponnusamy characterizing when the image f(D) under a quasiconformal harmonic univalent mapping is a John domain.

Date: 2020
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https://doi.org/10.1002/mana.201800256

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