Quasiconformal Extensions to Space of Weierstrass-Enneper LiftsReportar como inadecuado



 Quasiconformal Extensions to Space of Weierstrass-Enneper Lifts


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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.



Autor: Martin Chuaqui; Peter Duren; Brad Osgood

Fuente: https://archive.org/







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