Quantitative Localization and Comparison of Invariant Distances of Domains in $$\mathbb C^n$$

Abstract

We obtain explicit bounds on the difference between “local” and “global” Kobayashi distances in a domain of $$\mathbb C^n$$ as the points go toward a boundary point with appropriate geometric properties. We use this for the global comparison of various invariant distances. We provide some sharp estimates in dimension 1.