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


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 \( t \ge t_0 \).


Positive Constant Conjugacy Class Primitive Element Hyperbolic Group Gromov Hyperbolic Group 
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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:

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