, Volume 118, Issue 1, pp 109-124

Séries de poincaré des groupes géométriquement finis

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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.

Durant la rédaction de cet article, M. Peigné a bénéficié d'un détachement au Centre National de la Recherche Scientifique, URA 305.