Geometric & Functional Analysis GAFA

, Volume 12, Issue 3, pp 464–478

Growth of conjugacy classes in Gromov hyperbolic groups

Authors

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

DOI: 10.1007/s00039-002-8254-8

Cite this article as:
Coornaert, M. & Knieper, G. GAFA, Geom. funct. anal. (2002) 12: 464. doi:10.1007/s00039-002-8254-8

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 \( t \ge t_0 \).

Copyright information

© Birkhäuser Verlag, Basel 2002