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arXiv · 2104.11988

Complex geodesics and complex Monge--Amp\`{e}re equations with boundary singularity II

Xieping Wang
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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--Amp\`{e}re 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.

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Xieping Wang. 2021-04-24. Complex geodesics and complex Monge--Amp\`{e}re equations with boundary singularity II. https://doi.org/10.1512/iumj.2024.73.60021

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