2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78798A 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. In previous work, the author has proven the conjecture for $I$-bundles over a closed surface, taking into account the possibility of cusps. In this paper, we establish the conjecture in the case that M is a book of I-bundles or an acylindrical, hyperbolizable 3-manifold. In particular, we show that if M is a book of I-bundles, then the bound on injectivity radius depends on the number of generators in the fundamental group of M.23 pages, 1 figureGeometric TopologyGeneral Topology57M50 (Primary); 30F40, 57N10 (Secondary)text