# Logharmonic mappings on linearly connected domains

Logharmonic mappings on linearly connected domains A logharmonic mapping f is a mapping that is a solution of the nonlinear elliptic partial differential equation $$\dfrac{\overline{f_{ \overline{z}}}}{\overline{f}}=a\dfrac{f_{z}}{f}$$ f z ¯ ¯ f ¯ = a f z f . In this paper we investigate the univalence of logharmonic mappings of the form $$f=zH\overline{G},$$ f = z H G ¯ , where H and G are analytic on a linearly connected domain. We discuss the relation with the univalence of its analytic counterparts. Stable Univalence and its consequences are also considered. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

# Logharmonic mappings on linearly connected domains

, Volume 9 (2) – May 22, 2019
9 pages

/lp/springer-journals/logharmonic-mappings-on-linearly-connected-domains-CKqsborXQA
Publisher
Springer Journals
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-019-00318-6
Publisher site
See Article on Publisher Site

### Abstract

A logharmonic mapping f is a mapping that is a solution of the nonlinear elliptic partial differential equation $$\dfrac{\overline{f_{ \overline{z}}}}{\overline{f}}=a\dfrac{f_{z}}{f}$$ f z ¯ ¯ f ¯ = a f z f . In this paper we investigate the univalence of logharmonic mappings of the form $$f=zH\overline{G},$$ f = z H G ¯ , where H and G are analytic on a linearly connected domain. We discuss the relation with the univalence of its analytic counterparts. Stable Univalence and its consequences are also considered.

### Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: May 22, 2019