TWO-POINT DISTORTION THEOREMS FOR HARMONIC MAPPINGS
No Thumbnail Available
Date
2009
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
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 R(n) are given, thereby recasting a recent injectivity criterion of Chuaqui and Gevirtz in quantitative form.