  Closed hyperbolic manifolds are proven to minimize volume over all Alexandrov
spaces with curvature bounded below by -1 in the same bilipschitz class. As a
corollary compact convex cores with totally geodesic boundary are proven to
minimize volume over all hyperbolic manifolds in the same bilipschitz class.
Also, closed hyperbolic manifolds minimize volume over all hyperbolic cone
manifolds in the same bilipschitz class with cone angles not greater than 2pi.
The proof uses techniques developed by Besson-Courtois-Gallot. In 3 dimensions,
this result provides a partial solution to a conjecture in Kleinian groups
concerning acylindrical manifolds.
