Quasiconformal Extensions to Space of Weierstrass-Enneper Lifts
Complex Variables
2014-04-17 v2
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.
Keywords
Cite
@article{arxiv.1304.4198,
title = {Quasiconformal Extensions to Space of Weierstrass-Enneper Lifts},
author = {Martin Chuaqui and Peter Duren and Brad Osgood},
journal= {arXiv preprint arXiv:1304.4198},
year = {2014}
}