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

QUASICONFORMAL HARMONIC FUNCTIONS BETWEEN CONVEX DOMAINSDavid KalajPrirodnomatematicki fakultet, Podgorica, Serbia and MontenegroAbstract: 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 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 17 Dec 2004. This page was last modified: 9 Feb 2005.
© 2004 Mathematical Institute of the Serbian Academy of Science and Arts
