Complex geodesics and complex Monge--Ampère equations with boundary singularity II

Abstract

We study the parameter dependence of complex geodesics with prescribed boundary value and direction on bounded strongly linearly convex domains. As an important application we establish a quantitative relationship between the regularity of the pluricomplex Poisson kernel of such a domain, which is a solution to a homogeneous complex Monge--Ampère equation with boundary singularity, and the regularity of the boundary of the domain. Our results greatly improve the previous results of Chang--Hu--Lee and Bracci--Patrizio in this direction.

27 pages; final version