Pseudoconvexity and Gromov hyperbolicity

We give an estimate for the distance functions related to the Bergman, Caratheodory, and Kobayashi metrics on a bounded strictly pseudoconvex domain with C-2-smooth boundary. Our formula relates the distance function on the domain with the Carnot-Caratheodory metric on the boundary. As a corollary we conclude that the domain equipped with the any of the standard invariant distances is hyperbolic in the sense of Gromov. When the boundary of the domain is C-3-smooth, our estimate is exact up to a fixed additive term. (C) Academie des Sciences/Elsevier, Paris.