Annales Academię Scientiarum Fennicę
Mathematica
Volumen 33, 2008, 261-271

ON HARMONIC QUASICONFORMAL SELF-MAPPINGS OF THE UNIT BALL

David Kalaj

University of Montenegro, Faculty of Natural Sciences and Mathematics
Cetinjski put b.b. 81000 Podgorica, Montenegro; davidk 'at' cg.yu

Abstract. It is proved that any family of harmonic K-quasiconformal mappings {u = P[f], u(0) = 0} of the unit ball onto itself is a uniformly Lipschitz family providing that f\in C^1,\alpha. Moreover, the Lipschitz constant tends to 1 as K -> 1.

2000 Mathematics Subject Classification: Primary 30C65; Secondary 31B05.

Key words: Quasiconformal harmonic maps, Lipschitz condition.

Reference to this article: D. Kalaj: On harmonic quasiconformal self-mappings of the unit ball. Ann. Acad. Sci. Fenn. Math. 33 (2008), 261-271.

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