EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.)
Vol. 76(90), pp. 3–20 (2004)

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QUASICONFORMAL HARMONIC FUNCTIONS BETWEEN CONVEX DOMAINS

David Kalaj

Prirodno-matematicki fakultet, Podgorica, Serbia and Montenegro

Abstract: We generalize Martio's paper [14]. Indeed the problem studied in this paper is under which conditions on a homeomorphism $f$ between the unit circle $S^1:=\{z:|z|=1\}$ and a fix convex Jordan curve $\gamma$ the harmonic extension of $f$ is a quasiconformal mapping. In addition, we give some results for some classes of harmonic diffeomorphisms. Further, we give some results concerning harmonic quasiconformal mappings (which follow by the results obtained in [10]). Finally, we give some examples which explain that the classes defined in [14] are not big enough to enclose all harmonic quasiconformal mappings of the disc onto itself.

Keywords: complex functions; planar harmonic mappings

Classification (MSC2000): 30C55; 31A05

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Electronic fulltext finalized on: 17 Dec 2004. This page was last modified: 9 Feb 2005.

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