Let M be a complete hyperbolic 3-manifold with finitely generated fundamental group, and let H be its convex core. We show that there is an upper bound, depending only in the topology of M, on the radius of an embedded hyperbolic ball in H. As a consequence we deduce that strongly convergent finitely generated klienian groups have limit sets which converge in the Hausdorff topology.
First draft: May 2010. Revised: July 2011.
Groups, Geom. Dyn. 7 (2013) 109--126.