Discrete subgroups of small critical exponent

In this talk, I will present recent joint work with Beibei Liu. Let X be a simply connected, pinched negatively curved manifold, G be a finitely generated, torsion free, discrete subgroup of Isom(X). The critical exponent \delta(G) is defined to be the exponential growth rate of the number of G-orbit points inside a ball in X with respect to the radius. We show that if the critical exponent of G is small enough, then G is convex cocompact.