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arXiv · 1005.5333

Two-Point Distortion Theorems for Harmonic Mappings

Martin Chuaqui·Peter Duren·Brad Osgood
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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 ${\Bbb R}^n$ 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. 2010-05-28. Two-Point Distortion Theorems for Harmonic Mappings. https://arxiv.org/abs/1005.5333

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