Nehari‐type families of harmonic mappings | Zendy

Arbeláez Hugo | Zendy; Chuaqui Martin | Zendy; Sierra Willy | Zendy

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Nehari‐type families of harmonic mappings

Author(s) -

Arbeláez Hugo,

Chuaqui Martin,

Sierra Willy

Publication year - 2020

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.201800256

Subject(s) - mathematics , jacobian matrix and determinant , pure mathematics , injective function , affine transformation , converse , type (biology) , invariant (physics) , mathematical analysis , geometry , mathematical physics , ecology , biology

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.

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