Annales Academię Scientiarum Fennicę
Mathematica
Volumen 32, 2007, 579-594
The John Paul II Catholic University of Lublin,
Faculty of Mathematics and Natural Sciences
Al. Raclawickie 14, P.O. Box 129, 20-950 Lublin, Poland;
partyka 'at' kul.lublin.pl
Osaka City University, Department of Mathematics,
Graduate School of Science
Sugimoto, Sumiyoshi-ku, Osaka, 558, Japan;
ksakan 'at' sci.osaka-cu.ac.jp
Abstract. In the paper [13] Pavlovic proved that any quasiconformal and harmonic self-mapping F of the unit disk is bi-Lipschitz with respect to the Euclidean metric. We find explicit estimations of bi-Lipschitz constants for F that are expressed by means of the maximal dilatation K of F and |F-1(0)|. Under the additional assumption F(0) = 0 the estimations are asymptotically sharp as K \to 1, so F behaves almost like a rotation for sufficiently small K.
2000 Mathematics Subject Classification: Primary 30C55, 30C62.
Key words: Harmonic mappings, Poisson integral, Jacobian, quasiconformal mappings, Lipschitz condition, bi-Lipschitz condition.
Reference to this article: D. Partyka and K. Sakan: On bi-Lipschitz type inequalities for quasiconformal harmonic mappings. Ann. Acad. Sci. Fenn. Math. 32 (2007), 579-594.
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