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Geometric & Functional Analysis GAFA

, Volume 12, Issue 3, pp 464–478 | Cite as

Growth of conjugacy classes in Gromov hyperbolic groups

  • M. Coornaert
  • G. Knieper

Abstract.

Let \( \Gamma \) be a group acting properly and cocompactly by isometries on a proper geodesic \( \delta \)-hyperbolic metric space X whose boundary contains more than two points. Let P(t) denote the number of conjugacy classes of primitive elements \( \gamma \in \Gamma \) such that \( {\rm inf}_{x\in X}d(x,\gamma x) \le t \). We prove that there are positive constants A, B, h and t0 such that \( Ae^{ht}/t \le P(t) \le Be^{ht} \) for all \( t \ge t_0 \).

Keywords

Positive Constant Conjugacy Class Primitive Element Hyperbolic Group Gromov Hyperbolic Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag, Basel 2002

Authors and Affiliations

  • M. Coornaert
    • 1
  • G. Knieper
    • 2
  1. 1.Institut de Recherche Mathématique Avancée, Université Louis Pasteur et CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France, e-mail: coornaert@math.u-strasbg.frFR
  2. 2.Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany, e-mail: gknieper@math.ruhr-uni-bochum.deDE

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