Quasiconformal Extensions to Space of Weierstrass-Enneper Lifts

Martin Chuaqui; Peter Duren; Brad Osgood

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arXiv · 1304.4198

Quasiconformal Extensions to Space of Weierstrass-Enneper Lifts

Martin Chuaqui·Peter Duren·Brad Osgood

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Abstract

We derive a quasiconformal extension to 3-space of the Weierstrass-Enneper lifts of a class of harmonic mappings defined in the unit disk. The extension is based on fibrations of space by circles in domain and image that correspond to each other in a natural way. Convexity plays an essential role in the analysis. As a corollary we derive a sufficient condition for the underlying harmonic mapping to be univalent in the disk, with an explicit quasiconformal extension to the extended plane that generalizes the well known formula by Ahlfors-Weill.

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Martin Chuaqui, Peter Duren, Brad Osgood. 2013-04-15. Quasiconformal Extensions to Space of Weierstrass-Enneper Lifts. https://arxiv.org/abs/1304.4198

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