|Title:||Bounds for Jacobian of harmonic injective mappings in n-dimensional space||Journal:||Filomat||Volume:||29||Issue:||9||First page:||2119||Last page:||2124||Issue Date:||1-Jan-2015||Rank:||M21||ISSN:||0354-5180||DOI:||10.2298/FIL1509119B||Abstract:||
Using normal family arguments, we show that the degree of the first nonzero homogenous polynomial in the expansion of n dimensional Euclidean harmonic K-quasiconformal mapping around an internal point is odd, and that such a map from the unit ball onto a bounded convex domain, with K < 3n-1, is co-Lipschitz. Also some generalizations of this result are given, as well as a generalization of Heinz’s lemma for harmonic quasiconformal maps in Rn and related results.
|Keywords:||Convex codomains | Harmonic mappings | Quasiconformal mappings||Publisher:||Faculty of Sciences and Mathematics, University of Niš||Project:||Analysis and algebra with applications|
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