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

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Title: Growth of discrete groups of isometries in negative curvature: a gap-property
Alternate Title: Croissance des groupes discrets d'isométries en courbure strictement négative : un minorant universel
Authors: Besson, Gérard1 G.Besson@fourier.ujf-grenoble.fr, Courtois, Gilles2 courtois@math.polytechnique.fr, Gallot, Sylvestre1 Sylvestre.Gallot@fourier.ujf-grenoble.fr
Source: Comptes Rendus. Mathématique. Nov2005, Vol. 341 Issue 9, p567-572. 6p.
Subjects: Curvature, Nilpotent groups, Entropy, Hadamard matrices, Curves
Abstract (English): Abstract: We prove that a finitely generated group acting without fixed point on a n-dimensional Cartan–Hadamard manifold of pinched sectional curvature is either virtually nilpotent or has entropy . To cite this article: G. Besson et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005). [Copyright &y& Elsevier]
Abstract (French): Résumé: 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 est d''''entropie algébrique minorée, . Pour citer cet article : G. Besson et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).
Copyright of Comptes Rendus. Mathématique is the property of Academie des Science, Centre Mersenne and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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PubType: Academic Journal
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  Data: Growth of discrete groups of isometries in negative curvature: a gap-property
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  Data: Croissance des groupes discrets d'isométries en courbure strictement négative : un minorant universel
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  Data: Abstract: We prove that a finitely generated group acting without fixed point on a n-dimensional Cartan–Hadamard manifold of pinched sectional curvature is either virtually nilpotent or has entropy . To cite this article: G. Besson et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005). [Copyright &y& Elsevier]
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  Group: Ab
  Data: Résumé: 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 est d''''entropie algébrique minorée, . Pour citer cet article : G. Besson et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005). </ce:abst [Copyright 2005 Elsevier]
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  Data: <i>Copyright of Comptes Rendus. Mathématique is the property of Academie des Science, Centre Mersenne and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.crma.2005.09.025
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        Type: general
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      – TitleFull: Growth of discrete groups of isometries in negative curvature: a gap-property
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              Text: Nov2005
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