Parameter dependence of complex geodesics and its applications


الملخص بالإنكليزية

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 present a quantitative relationship between the regularity of the pluricomplex Poisson kernel of such a domain, which is a solution to a homogeneous complex Monge-Amp`{e}re equation with boundary singularity, and that of the boundary of the domain. Our results improve considerably previous ones in this direction due to Chang-Hu-Lee and Bracci-Patrizio.

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