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Univalence Criteria for Lifts of Harmonic Mappings to Minimal Surfaces

M. Chuaqui·P. Duren·B. Osgood
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Abstract

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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M. Chuaqui, P. Duren, B. Osgood. 2006-07-03. Univalence Criteria for Lifts of Harmonic Mappings to Minimal Surfaces. https://arxiv.org/abs/math/0607063

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