The Kobayashi metric and Gromov hyperbolicity on pseudoconvex domains of finite type in ${\mathbb{C}}^2$

Abstract

In this paper, we obtain a more precise estimate of Catlin-type distance for smoothly bounded pseudoconvex domain of finite type in ${\mathbb{C}}^2$. As an application, we get an alternative proof of the Gromov hyperbolicity of this domain equipped with the Kobayashi distance.