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

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

paper · doi:10.48550/arxiv.1410.5252

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.

Related

• On quasiconformal extensions of harmonic mappings associated with pre-Schwarzian derivative
• Criteria for univalence and quasiconformal extension for harmonic\n mappings on planar domains
• Schwarzian Derivatives and Uniform Local Univalence
• Quasiconformal extension for harmonic mappings on finitely connected\n domains
• Pre-Schwarzian and Schwarzian derivatives of harmonic mappings