Lower bounds on the Bergman metric near points of infinite type

Abstract

Let $\Omega$ be a pseudoconvex domain in ${\mathbb{C}}^n$ satisfying an $f$-property for some function $f$. We show that the Bergman metric associated to $\Omega$ has the lower bound $\tilde{g}({\delta }_{\Omega }(z{)}^{-1})$ where ${\delta }_{\Omega }(z)$ is the distance from $z$ to the boundary $\partial \Omega$ and $\tilde{g}$ is a specific function defined by $f$. This refines Khanh-Zampieri's work in \cite{KZ12} with reducing the smoothness assumption of the boundary.

13 pages