2010/05/28 by Martin Chuaqui, Peter Duren, Chuaqui, Martin +3
Mathematics · #53A10 #Complex Variables (math.CV) #FOS: Mathematics #Primary 30C99 #Secondary 31A05 #math.CV #msc:30C99 #msc:31A05 #msc:53A10
paper · pdf · doi:10.48550/arxiv.1005.5333
arxiv created 2010/05/28 · arxiv updated 2010/05/31
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 Rn are given, thereby recasting a recent injectivity criterion of Chuaqui and Gevirtz in quantitative form.