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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… Click to show full 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.
Keywords:
type families;
harmonic mappings;
nehari type;
families harmonic
Journal Title: Mathematische Nachrichten
Year Published: 2019
Link to full text (if available)
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Journal Title: Mathematische Nachrichten
Year Published: 2019
Link to full text (if available)
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recommendations!