Injectivity of harmonic mappings with a specified injective holomorphic part - Partyka, Dariusz; Sakan, Ken-ichi (Annales Fennici Mathematici, 2022)
Let \(F=H+G\) be a locally injective and sense-preserving harmonic mapping of the unit disk \(D\) in the complex plane \(C\), where \(H\) and \(G\) are holomorphic in \(D\) and \(G(0)=0\). The aim of this paper is studying interplay between properties of \(F_ε:=H+εG\), \(εC\), and its holomorphic part \(H\). In particular, several results dealing with the injectivity of \(F_ε\) are obtained.