Pluriharmonic Mappings with the Convex Holomorphic Part

Source abstract

In 2018, Partyka et al. established several equivalent conditions for a sense‐preserving locally injective harmonic mapping in the unit disk 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 , where h is a convex mapping in the unit ball and A ∈ L ( ℂ n , ℂ n ) with ‖ A ‖ = 1. Then, we establish a relationship of two‐point distortion property between f and f A .