Quasiconformal Harmonic Functions between Convex Domains
نویسنده
چکیده
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 S1 := {z : |z| = 1} and a fix convex Jordan curve γ 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.
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