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.
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Acknowledgements
The author would like to express his gratitude to Prof. Hervé Gaussier for his availability and for introducing him to Gromov hyperbolicity theory, and to Prof. Filippo Bracci for useful discussions and suggestions.
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Communicated by Ngaiming Mok.
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Partially supported by PRIN Real and Complex Manifolds: Topology, Geometry and holomorphic dynamics n. 2017JZ2SW5 and by MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C18000100006.
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Fiacchi, M. Gromov hyperbolicity of pseudoconvex finite type domains in \({\mathbb {C}}^2\). Math. Ann. 382, 37–68 (2022). https://doi.org/10.1007/s00208-020-02135-w
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DOI: https://doi.org/10.1007/s00208-020-02135-w