Growth of discrete groups of isometries in negative curvature: a gap-property

Gérard Besson; Gilles Courtois; Sylvestre Gallot

doi:10.1016/j.crma.2005.09.025

Differential Geometry/Group Theory

Growth of discrete groups of isometries in negative curvature: a gap-property

Presented by: Étienne Ghys

Gérard Besson ¹; Gilles Courtois ²; Sylvestre Gallot ¹

¹ Institut Fourier, université de Grenoble I, UMR 5582 CNRS-UJF, 38402 Saint-Martin-d'Hères, France
² École polytechnique, centre de mathématiques, UMR 7640 du CNRS, 91128 Palaiseau cedex, France

Comptes Rendus. Mathématique, Volume 341 (2005) no. 9, pp. 567-572.

Abstract
Résumé

We prove that a finitely generated group acting without fixed point on a n-dimensional Cartan–Hadamard manifold of pinched sectional curvature $- a^{2} ⩽ K ⩽ - 1$ is either virtually nilpotent or has entropy $Ent (Γ) ⩾ C (n, a) > 0$ .

Nous prouvons qu'un sous groupe de type fini Γ, non virtuellement nilpotent, du groupe des isométries d'une variété de Cartan–Hadamard de dimension n et de courbure sectionnelle vérifiant $- a^{2} ⩽ K ⩽ - 1$ est d'entropie algébrique minorée, $Ent (Γ) ⩾ C (n, a) > 0$ .

Received: 2005-07-06
Accepted: 2005-09-11
Published online: 2005-10-11

DOI: 10.1016/j.crma.2005.09.025

Author's affiliations:

Gérard Besson ¹; Gilles Courtois ²; Sylvestre Gallot ¹

¹ Institut Fourier, université de Grenoble I, UMR 5582 CNRS-UJF, 38402 Saint-Martin-d'Hères, France
² École polytechnique, centre de mathématiques, UMR 7640 du CNRS, 91128 Palaiseau cedex, France

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     author = {G\'erard Besson and Gilles Courtois and Sylvestre Gallot},
     title = {Growth of discrete groups of isometries in negative curvature: a gap-property},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {567--572},
     publisher = {Elsevier},
     volume = {341},
     number = {9},
     year = {2005},
     doi = {10.1016/j.crma.2005.09.025},
     language = {en},
}

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Gérard Besson; Gilles Courtois; Sylvestre Gallot. Growth of discrete groups of isometries in negative curvature: a gap-property. Comptes Rendus. Mathématique, Volume 341 (2005) no. 9, pp. 567-572. doi : 10.1016/j.crma.2005.09.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.09.025/

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