Séries de poincaré des groupes géométriquement finis
- Cite this article as:
- Dal'bo, F., Otal, JP. & Peigné, M. Isr. J. Math. (2000) 118: 109. doi:10.1007/BF02803518
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.