Harmonic mappings and distance function

Details Harmonic mappings and distance function Harmonic mappings and distance function

2010-11-12

arxiv.org/abs/1011.3012v1

Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), Vol. X (2011), 669-681

Mathematics

Complex Variables

10 pages, to appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze

Scientific paper

We prove the following theorem: every quasiconformal harmonic mapping between two plane domains with $C^{1,\alpha}$ ($\alpha<1$), respectively $C^{1,1}$ compact boundary is bi-Lipschitz. The distance function with respect to the boundary of the image domain is used. This in turn extends a similar result of the author in \cite{kalajan} for Jordan domains, where stronger boundary conditions for the image domain were needed.

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