Groups, Geometry, and Dynamics
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Published online: 2013-01-31
An upper bound for injectivity radii in convex coresBrian H. Bowditch (1) University of Warwick, Coventry, United Kingdom
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.
Keywords: Hyperbolic 3-manifold, convex core, injectivity radius
Bowditch Brian: An upper bound for injectivity radii in convex cores. Groups Geom. Dyn. 7 (2013), 109-126. doi: 10.4171/GGD/178