Criteria for univalence and quasiconformal extension of harmonic mappings in terms of the Schwarzian DERIVATIVE

2014/10/20 by Rodrigo Hernández, María J. Martín, Hernández, Rodrigo +1 · 1 citation
Mathematics · #30C55 #30C62 #31A05 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30C55 #msc:30C62 #msc:31A05

paper · pdf · doi:10.48550/arxiv.1410.5252

arxiv created 2014/10/20 · arxiv updated 2014/10/21

Abstract

We prove that if the Schwarzian norm of a given complex-valued locally univalent harmonic mapping f in the unit disk is small enough, then f is, indeed, globally univalent and can be extended to a quasiconformal mapping in the extended complex plane.

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