Lower bounds on the Bergman metric near points of infinite type
Let $Ω$ be a pseudoconvex domain in $\mathbb C^n$ satisfying an $f$-property for some function $f$. We show that the Bergman metric associated to $Ω$ has the lower bound $\tilde g(δ_Ω(z)^{-1})$ where $δ_Ω(z)$ is the distance from $z$ to the boundary $\partialΩ$ 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.
math.CV↗