Asymptotic behaviour of the Bergman kernel and metric

Abstract

We prove nontangential asymptotic limits of the Bergman kernel on the diagonal, and the Bergman metric and its holomorphic sectional curvature at exponentially flat infinite type boundary points of smooth bounded pseudoconvex domains in $\mathbb{C}^{n+1}$, $n\in\mathbb{N}$. We first show that these objects satisfy appropriate localizations and then use the method of scaling to complete the proof.