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On the Gromov Hyperbolicity of Convex Domains in \({\mathbb {C}}^n\)

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Abstract

We prove that if a \({\mathcal {C}}^\infty \)-smooth bounded convex domain in \({\mathbb {C}}^n\) contains a holomorphic disc in its boundary, then the domain is not Gromov hyperbolic for the Kobayashi distance. We also give examples of bounded smooth convex domains that are not strongly pseudoconvex but are Gromov hyperbolic.

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Acknowledgements

We would like to thank the referee for valuable comments and suggestions that considerably improved the exposition.

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Authors and Affiliations

  1. Univ. Grenoble Alpes, CNRS, IF, 38000, Grenoble, France

    Hervé Gaussier

  2. Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India

    Harish Seshadri

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  1. Hervé Gaussier
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  2. Harish Seshadri
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Correspondence to Hervé Gaussier.

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Communicated by Mario Bonk.

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Gaussier, H., Seshadri, H. On the Gromov Hyperbolicity of Convex Domains in \({\mathbb {C}}^n\). Comput. Methods Funct. Theory 18, 617–641 (2018). https://doi.org/10.1007/s40315-018-0243-5

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  • DOI: https://doi.org/10.1007/s40315-018-0243-5

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