On the Univalence and Quasiconformal Extensions Criterion for Harmonic Mappings Associated with Pre-Schwarzian Derivative

Abstract

As a generalization of Ahlfors’s results for analytic functions, by using the pre-Schwarzian derivative of harmonic mappings, the authors obtain a criterion of univalence and quasiconformal extension for harmonic functions. As applications, they give a lower bound of the inner radius of univalency by means of pre-Schwarzian derivative of harmonic mappings for a planar domain.

Keywords

Harmonic mapping / Quasiconformal extension / Pre-Schwarzian derivative / Inner radius of univalency / 30C55 / 31C45 / 30C62 / 31A05

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