Quasiconformal Extensions to Space of Weierstrass-Enneper Lifts
| Autor: | Chuaqui, Martin, Duren, Peter, Osgood, Brad |
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| Rok vydání: | 2013 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. |
| Databáze: | arXiv |
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