Injectivity of harmonic mappings with a specified injective holomorphic part | Zendy

Dariusz Partyka | Zendy; Ken-ichi Sakan | Zendy

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Injectivity of harmonic mappings with a specified injective holomorphic part

Author(s) -

Dariusz Partyka,

Ken-ichi Sakan

Publication year - 2022

Publication title -

annales fennici mathematici

Language(s) - English

Resource type - Journals

eISSN - 2737-114X

pISSN - 2737-0690

DOI - 10.54330/afm.115432

Subject(s) - holomorphic function , injective function , unit disk , mathematics , harmonic , harmonic function , complex plane , plane (geometry) , unit (ring theory) , pure mathematics , combinatorics , mathematical analysis , physics , geometry , quantum mechanics , mathematics education

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.

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