Geodesic
Quasiconformal Harmonic Functions Between Convex Domains
Publications de l'Institut Mathématique, _N_S_76 (2004) no. 90, p. 3

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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.
Classification : 30C55 31A05
Keywords: complex functions, planar harmonic mappings 
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     title = {Quasiconformal {Harmonic} {Functions} {Between} {Convex} {Domains}},
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David Kalaj. Quasiconformal Harmonic Functions Between Convex Domains. Publications de l'Institut Mathématique, _N_S_76 (2004) no. 90, p. 3 . http://geodesic.mathdoc.fr/item/PIM_2004_N_S_76_90_a0/