On the growth of nonuniform lattices in pinched negatively curved manifolds

Françoise Dal'Bo-Milonet (1) , Marc Peigné (2) , Jean-Claude Picaud (2) , Andrea Sambusetti (3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LMPT - Laboratoire de Mathématiques et Physique Théorique
3 UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome]

We study the relation between the exponential growth rate of volume in a pinched negatively curved manifold and the critical exponent of its lattices. These objects have a long and interesting story and are closely related to the geometry and the dynamical properties of the geodesic flow of the manifold .

Domaines: Systèmes dynamiques [math.DS]

Françoise Dal'Bo-Milonet, Marc Peigné, Jean-Claude Picaud, Andrea Sambusetti. On the growth of nonuniform lattices in pinched negatively curved manifolds. Journal für die reine und angewandte Mathematik, 2009, 2009 (627), pp.31-52. ⟨10.1515/CRELLE.2009.010⟩. ⟨hal-00360859⟩