Convex-cocompactness of Kleinian groups and conformally flat manifolds with positive scalar curvature

We give a sufficient condition for a higher dimensional Kleinian group Γ ⊂ Isom(ℍⁿ⁺¹) to be convex cocompact in terms of the critical exponent of Γ. As a consequence, we see that the fundamental group of a compact conformally flat manifold with positive scalar curvature is hyperbolic in the sense of Gromov. We give some other applications to geometry and topology of conformally flat manifolds with positive scalar curvature.