Hyperbolic convex cores and simplicial volume

Abstract

This article investigates the relationship between the topology of hyperbolizable $3$-manifolds $M$ with incompressible boundary and the volume of hyperbolic convex cores homotopy equivalent to $M$. Specifically, it proves a conjecture of Bonahon stating that the volume of a convex core is at least half the simplicial volume of the doubled manifold $\mathrm{DM}$, and this inequality is sharp. This article proves that the inequality is, in fact, sharp in every pleating variety of AH$(M)$