Differential Geometry/Group Theory
Growth of discrete groups of isometries in negative curvature: a gap-property
Comptes Rendus. Mathématique, Volume 341 (2005) no. 9, pp. 567-572.

We prove that a finitely generated group acting without fixed point on a n-dimensional Cartan–Hadamard manifold of pinched sectional curvature a2K1 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 a2K1 est d'entropie algébrique minorée, Ent(Γ)C(n,a)>0.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2005.09.025
Besson, Gérard 1; Courtois, Gilles 2; Gallot, Sylvestre 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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Besson, Gérard; Courtois, Gilles; Gallot, Sylvestre. 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. http://www.numdam.org/articles/10.1016/j.crma.2005.09.025/

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