Let be a complete hyperbolic 3-manifold with finitely generated fundamental group, and let be its convex core. We show that there is an upper bound on the radius of an embedded hyperbolic ball in , which depends only on the topology of . As a consequence, we deduce that limit sets of strongly convergent kleinian groups converge.
Cite this article
Brian H. Bowditch, An upper bound for injectivity radii in convex cores. Groups Geom. Dyn. 7 (2013), no. 1, pp. 109–126DOI 10.4171/GGD/178