Two-Point Distortion Theorems for Harmonic Mappings
Complex Variables
2010-05-31 v1
Abstract
In earlier work the authors have extended Nehari's well-known Schwarzian derivative criterion for univalence of analytic functions to a univalence criterion for canonical lifts of harmonic mappings to minimal surfaces. The present paper develops some quantitative versions of that result in the form of two-point distortion theorems. Along the way some distortion theorems for curves in are given, thereby recasting a recent injectivity criterion of Chuaqui and Gevirtz in quantitative form.
Cite
@article{arxiv.1005.5333,
title = {Two-Point Distortion Theorems for Harmonic Mappings},
author = {Martin Chuaqui and Peter Duren and Brad Osgood},
journal= {arXiv preprint arXiv:1005.5333},
year = {2010}
}