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

arXiv: Complex Variables
Apr 2020

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.

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