Estimates of Invariant Metrics on Pseudoconvex Domains of Finite Type in C 3

Abstract EN

Let Ω be a smoothly bounded pseudoconvex domain in C 3 and assume that z 0 ∈ b Ω is a point of finite 1-type in the sense of D’Angelo.

Then, there are an admissible curve Γ ⊂ Ω ∪ { z 0 } , connecting points q 0 ∈ Ω and z 0 ∈ b Ω , and a quantity M ( z , X ) , along z ∈ Γ , which bounds from above and below the Bergman, Caratheodory, and Kobayashi metrics in a small constant and large constant sense.