Lower Bounds on the Bergman Metric Near Points of Infinite Type

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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 with Ω has the lower bound $\tilde {g}(\delta _{\Omega }(z)^{-1})$ where δΩ(z) is the distance from z to the boundary ∂Ω and $\tilde g$ is a specific function defined by f. This refines Khanh–Zampieri’s work in Khanh and Zampieri (Invent. Math. 188, 729–750, 2012) with weaker smoothness assumption of the boundary.