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Logharmonic mappings on linearly connected domains

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Abstract

A logharmonic mapping f is a mapping that is a solution of the nonlinear elliptic partial differential equation \(\dfrac{\overline{f_{ \overline{z}}}}{\overline{f}}=a\dfrac{f_{z}}{f}\). In this paper we investigate the univalence of logharmonic mappings of the form \( f=zH\overline{G},\) 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.

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  1. Mathematics Division, American University in Dubai (AUD), P.O. Box 28282, Dubai, UAE

    Layan El Hajj

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  1. Layan El Hajj
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Correspondence to Layan El Hajj.

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El Hajj, L. Logharmonic mappings on linearly connected domains. Anal.Math.Phys. 9, 829–837 (2019). https://doi.org/10.1007/s13324-019-00318-6

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  • DOI: https://doi.org/10.1007/s13324-019-00318-6

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