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Pluriharmonic Mappings with the Convex Holomorphic Part

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  • Ma Lihua
  • See Keong Lee
  • Kenan Yildirim

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.

Suggested Citation

  • Ma Lihua & See Keong Lee & Kenan Yildirim, 2022. "Pluriharmonic Mappings with the Convex Holomorphic Part," Journal of Mathematics, Hindawi, vol. 2022, pages 1-9, December.
    • Handle: RePEc:hin:jjmath:3450575
    DOI: 10.1155/2022/3450575
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