Pluriharmonic Mappings with the Convex Holomorphic Part - Ma Lihua; See Keong Lee (Journal of Mathematics)
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.