Estimates of the Kobayashi metric and Gromov hyperbolicity on convex domains of finite type

Abstract

In this paper, we give a local estimate for the Kobayashi distance on a bounded convex domain of finite type, which relates to a local pseudodistance near the boundary. The estimate is precise up to a bounded additive term. Also, we conclude that the domain equipped with the Kobayashi distance is Gromov hyperbolic that gives another proof of the result of Zimmer.