Asymptotic Behavior of the Bergman Metric at Infinite Type Points

Abstract

We investigate 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 $C^{n+1}$, $n\in N$. After showing that these objects satisfy the appropriate localizations, we apply the method of scaling to prove our results.