Gromov hyperbolicity of pseudoconvex finite type domains in $\mathbb{C}^2$

Abstract

We prove that every bounded smooth domain of finite d'Angelo type in $\mathbb{C}^2$ endowed with the Kobayashi distance is Gromov hyperbolic and its Gromov boundary is canonically homeomorphic to the Euclidean boundary. We also show that any domain in $\mathbb{C}^2$ endowed with the Kobayashi distance is Gromov hyperbolic provided there exists a sequence of automorphisms that converges to a smooth boundary point of finite D'Angelo type.