Two-point distortion theorems for harmonic and pluriharmonic mappings

Duren, Peter; Hamada, Hidetaka; Kohr, Gabriela

doi:10.1090/S0002-9947-2011-05596-0

Two-point distortion theorems for harmonic and pluriharmonic mappings
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by Peter Duren, Hidetaka Hamada and Gabriela Kohr PDF

Trans. Amer. Math. Soc. 363 (2011), 6197-6218 Request permission

Abstract:

Two-point distortion theorems are obtained for affine and linearly invariant families of harmonic mappings on the unit disk, with generalizations to pluriharmonic mappings of the unit ball in ${\mathbb {C}}^{n}$. In particular, necessary and sufficient conditions are given for a locally univalent harmonic or pluriharmonic mapping to be univalent. Some particular subclasses are also considered.

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