  This paper 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 DM, and this inequality is sharp.
This paper proves that the inequality is in fact sharp in every pleating
variety of AH(M).
