Bounds for Jacobian of harmonic injective mappings in n-dimensional space

Vladimir Bozin, Miodrag Mateljevic
2015 Filomat  
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 < 3 n−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 R n and related results.
doi:10.2298/fil1509119b fatcat:me46uu2scbcyphhbqtio4bxxwa