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Israel Journal of Mathematics

, Volume 118, Issue 1, pp 109–124 | Cite as

Séries de poincaré des groupes géométriquement finis

  • Françoise Dal'boEmail author
  • Jean-Pierre Otal
  • Marc Peigné
Article

Abstract

In this paper, we study the behaviour of the Poincaré series of a geometrically finite group Γ of isometries of a riemannian manifoldX with pinched curvature, in the case when Γ contains parabolic elements. We give a sufficient condition on the parabolic subgroups of Γ in order that Γ be of divergent type. When Γ is of divergent type, we show that the Sullivan measure on the unit tangent bundle ofX/Γ is finite if and only if certain series which involve only parabolic elements of Γ are convergent. We build also examples of manifoldsX on which geometrically finite groups of convergent type act.

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Copyright information

© Hebrew University 2000

Authors and Affiliations

  • Françoise Dal'bo
    • 1
    Email author
  • Jean-Pierre Otal
    • 2
  • Marc Peigné
    • 1
  1. 1.Université de Rennes IIRMARRennes CedexFrance
  2. 2.Ecole Normale Supérieure de LyonLyon Cedex 07France

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