BOUNDS FOR JACOBIAN OF HARMONIC INJECTIVE MAPPINGS IN N-DIMENSIONAL SPACE

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.