An upper bound for injectivity radii in convex cores

Abstract

Let $N$ 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 on the radius of an embedded hyperbolic ball in $H$ , which depends only on the topology of $N$ . As a consequence, we deduce that limit sets of strongly convergent kleinian groups converge.