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

TL;DR

This paper provides a local estimate for the Kobayashi distance on convex domains of finite type, demonstrating Gromov hyperbolicity and offering a new proof of Zimmer's result.

Contribution

It introduces a precise local estimate for the Kobayashi distance and establishes Gromov hyperbolicity for these domains, enhancing understanding of their geometric properties.

Findings

Kobayashi distance estimate relates to boundary pseudodistance

Convex domains of finite type are Gromov hyperbolic

Provides an alternative proof of Zimmer's hyperbolicity result

Abstract

In this paper we give an 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 which gives another proof of the result of Zimmer.