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Gromov Hyperbolicity of Bounded Convex Domains

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Metrical and Dynamical Aspects in Complex Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2195))

Abstract

In this chapter we describe some results on Gromov hyperbolicity in several complex variables. In particular, we prove that the Kobayashi metric on a smoothly bounded convex domain is Gromov hyperbolic if and only if the domain has finite type and we provide a proof that the Kobayashi metric is Gromov hyperbolic on a strongly pseudoconvex domain. We will also describe connections between the Kobayashi metric and Hilbert metric and then describe recent work of Benoist concerning the Gromov hyperbolicity of the Hilbert metric. Finally, we list a number of open problems.

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Acknowledgements

This material is based upon work supported by the National Science Foundation under Grant Number NSF 1400919.

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  1. Department of Mathematics, College of William and Mary, Williamsburg, VA, 23185, USA

    Andrew Zimmer

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  1. Andrew Zimmer
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Correspondence to Andrew Zimmer .

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  1. Laboratoire Paul Painlevé, Université de Lille, Villeneuve d’Ascq, France

    Léa Blanc-Centi

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Zimmer, A. (2017). Gromov Hyperbolicity of Bounded Convex Domains. In: Blanc-Centi, L. (eds) Metrical and Dynamical Aspects in Complex Analysis. Lecture Notes in Mathematics, vol 2195. Springer, Cham. https://doi.org/10.1007/978-3-319-65837-7_4

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