Estimates of Invariant Metrics on Pseudoconvex Domains of Finite Type inC3

摘要

LetΩbe a smoothly bounded pseudoconvex domain inC3and assume thatz0∈bΩis a point of finite 1-type in the sense of D’Angelo. Then, there are an admissible curveΓ⊂Ω∪{z0}, connecting points  q0∈Ωandz0∈bΩ, and a quantityM(z,X), alongz∈Γ, which bounds from above and below the Bergman, Caratheodory, and Kobayashi metrics in a small constant and large constant sense.