Univalence Criteria for Lifts of Harmonic Mappings to Minimal Surfaces

Details Univalence Criteria for Lifts of Harmonic Mappings to Minimal Surfaces Univalence Criteria for Lifts of Harmonic Mappings to Minimal Surfaces

2006-07-03

arxiv.org/abs/math/0607063v1

Mathematics

Complex Variables

Scientific paper

A general criterion in terms of the Schwarzian derivative is given for global univalence of the Weierstrass--Enneper lift of a planar harmonic mapping. Results on distortion and boundary regularity are also deduced. Examples are given to show that the criterion is sharp. The analysis depends on a generalized Schwarzian defined for conformal metrics and on a Schwarzian introduced by Ahlfors for curves. Convexity plays a central role.

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