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A Schwarz-Pick inequality for harmonic quasiconformal mappings and its applications. (English) Zbl 1194.30027
Summary: The main result of this paper is the sharp generalized Schwarz-Pick inequality for Euclidean harmonic quasiconformal mappings with convex ranges, which generalizes a result given by Mateljević. As an applications, we obtain the property of quasi-isometry with respect to the Poincaré distance and an analogue of the Koebe theorem for this class of mappings.

MSC:
30C62 Quasiconformal mappings in the complex plane
31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
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