Univalence Criteria for Lifts of Harmonic Mappings to Minimal Surfaces

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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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Complex Variables, Differential Geometry, 30C99 ; 31A05; 53A10

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http://salesiana.dossiersoluciones.com/handle/123456789/114130

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0607063
 http://arxiv.org/abs/math/0607063

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arXiv