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Winter 2009 Two-point distortion theorems for harmonic mappings
Martin Chuaqui, Peter Duren, Brad Osgood
Illinois J. Math. 53(4): 1061-1075 (Winter 2009). DOI: 10.1215/ijm/1290435339

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 ℝn are given, thereby recasting a recent injectivity criterion of Chuaqui and Gevirtz in quantitative form.

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Martin Chuaqui. Peter Duren. Brad Osgood. "Two-point distortion theorems for harmonic mappings." Illinois J. Math. 53 (4) 1061 - 1075, Winter 2009. https://doi.org/10.1215/ijm/1290435339

Information

Published: Winter 2009
First available in Project Euclid: 22 November 2010

zbMATH: 1207.30035
MathSciNet: MR2741178
Digital Object Identifier: 10.1215/ijm/1290435339

Subjects:
Primary: 30C99
Secondary: 31A05 , 53A10

Rights: Copyright © 2009 University of Illinois at Urbana-Champaign

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Vol.53 • No. 4 • Winter 2009
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