1999/07/08 by Carol E. Fan, Fan, Carol E.
Mathematics · #30F40 #57M50 (primary) #57N10 (Secondary) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.GT #msc:30F40 #msc:57M50 #msc:57N10
paper · pdf · doi:10.48550/arxiv.math/9907052
42 pages, 6 figures
arxiv created 1999/07/08 · openalex publication_date 1999/07/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A version of a conjecture of McMullen is as follows: Given a hyperbolizable 3-manifold M with incompressible boundary, there exists a uniform constant K such that if N is a hyperbolic 3-manifold homeomorphic to the interior of M, then the injectivity radius based at points in the convex core of N is bounded above by K. This conjecture suggests that convex cores are uniformly congested. We will give a proof in the case when M is an I-bundle over a closed surface, taking into account the possibility of cusps.