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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.