Geodesic
Injectivity of harmonic mappings with a specified injective holomorphic part
Dariusz Partyka1 ; Ken-ichi Sakan2
1 The John Paul II Catholic University of Lublin, Department of Mathematical Analysis, and The State School of Higher Education in Chełm, Institute of Mathematics and Information Technology
2 Osaka Metropolitan University, Graduate School of Science
Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 573-586.

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Let $F=H+\overline{G}$ be a locally injective and sense-preserving harmonic mapping of the unit disk $\mathbb{D}$ in the complex plane $\mathbb{C}$, where $H$ and $G$ are holomorphic in $\mathbb{D}$ and $G(0)=0$. The aim of this paper is studying interplay between properties of $F_\varepsilon:=H+\varepsilon\overline G$, $\varepsilon\in\mathbb{C}$, and its holomorphic part $H$. In particular, several results dealing with the injectivity of $F_\varepsilon$ are obtained.
DOI : 10.54330/afm.115432
Keywords: Harmonic mappings, quasiconformal mappings, Lipschitz condition, bi-Lipschitz condition, co-Lipschitz condition, injectivity of harmonic mappings

Dariusz Partyka 1 ; Ken-ichi Sakan 2

1 The John Paul II Catholic University of Lublin, Department of Mathematical Analysis, and The State School of Higher Education in Chełm, Institute of Mathematics and Information Technology
2 Osaka Metropolitan University, Graduate School of Science 
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Dariusz Partyka; Ken-ichi Sakan. Injectivity of harmonic mappings with a specified injective holomorphic part. Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 573-586. doi : 10.54330/afm.115432. http://geodesic.mathdoc.fr/articles/10.54330/afm.115432/

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