Logharmonic mappings on linearly connected domains

A logharmonic mapping f is a mapping that is a solution of the nonlinear elliptic partial differential equation f z ¯ ¯ f ¯ = a f z f . In this paper we investigate the univalence of logharmonic mappings of the form f = z H G ¯ , where H and G are analytic on a linearly connected domain. We discuss...

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Veröffentlicht in:	Analysis and mathematical physics 2019-06, Vol.9 (2), p.829-837
1. Verfasser:	El Hajj, Layan
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Domains Mapping Mathematical Methods in Physics Mathematics Mathematics and Statistics Partial differential equations
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Zusammenfassung:	A logharmonic mapping f is a mapping that is a solution of the nonlinear elliptic partial differential equation f z ¯ ¯ f ¯ = a f z f . In this paper we investigate the univalence of logharmonic mappings of the form 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.
ISSN:	1664-2368 1664-235X
DOI:	10.1007/s13324-019-00318-6