On the Gromov hyperbolicity of domains in $\protect \mathbb{C}^n$

Hervé Gaussier

doi:10.5802/tsg.362

On the Gromov hyperbolicity of domains in

ℂ^{n}

Hervé Gaussier ¹

¹ Université Grenoble Alpes, CNRS, IF, F-38000 Grenoble, (France)

Séminaire de théorie spectrale et géométrie, Volume 35 (2017-2019), pp. 23-42.

Abstract

We present several recent results dealing with the metric properties of domains in the complex Euclidean space $ℂ^{n}$ . We provide with examples of domains, endowed with Finsler or Kähler metrics, that are (or are not) Gromov hyperbolic. We also present how different notions, such as the Gromov hyperbolicity, the holomorphic bisectional curvature or the d’Angelo type may be related for smooth bounded domains in $ℂ^{n}$ . We also present several open questions in the core of the paper.

Published online: 2021-04-21

DOI: 10.5802/tsg.362

Classification: 32Q05, 32Q45, 53C23
Keywords: Complex manifolds, Finsler metric, Kähler metric, Gromov hyperbolicity, holomorphic bisectional curvature, d’Angelo finite type

Author's affiliations:

Hervé Gaussier ¹

¹ Université Grenoble Alpes, CNRS, IF, F-38000 Grenoble, (France)

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Hervé Gaussier. On the Gromov hyperbolicity of domains in $\protect \mathbb{C}^n$. Séminaire de théorie spectrale et géométrie, Volume 35 (2017-2019), pp. 23-42. doi : 10.5802/tsg.362. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.362/

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