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

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.

References in corpus (1)

• Affine and linear invariant families of harmonic mappings