Univalence criteria for lifts of harmonic mappings to minimal surfaces
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Date
2007
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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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Keywords
harmonic mapping, Schwarzian derivative, curvature, minimal surface