Lower Bounds on the Bergman Metric Near Points of Infinite Type

Let Ω be a pseudoconvex domain in ℂ^n satisfying an f -property for some function f . We show that the Bergman metric associated with Ω has the lower bound g̃(δ _Ω(z)^-1) where δ Ω ( z ) is the distance from z to the boundary ∂ Ω and g̃ 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.