Pluriharmonic Mappings with the Convex Holomorphic Part

Ma Lihua, See Keong Lee and Kenan Yildirim

Journal of Mathematics, 2022, vol. 2022, 1-9

Abstract: In 2018, Partyka et al. established several equivalent conditions for a sense-preserving locally injective harmonic mapping f=h+g¯ in the unit disk D with convex holomorphic part h to be quasiconformal in terms of the relationships of two-point distortion of h, g, and f. In this study, we first generalize the above result to the case of pluriharmonic mappings fA=h+Ag¯, where h is a convex mapping in the unit ball Bn and A∈Lℂn,ℂn with A=1. Then, we establish a relationship of two-point distortion property between f and fA.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:3450575

DOI: 10.1155/2022/3450575

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