Resumen de The barycenter method on singular spaces

Peter A. Storm

• Compact convex cores with totally geodesic boundary are proven to uniquely minimize volume over all hyperbolic 3-manifolds in the same homotopy class. This solves a conjecture in Kleinian groups concerning acylindrical 3-manifolds. Closed hyperbolic manifolds are proven to uniquely minimize volume over all compact hyperbolic cone-manifolds in the same homotopy class with cone angles =2p. Closed hyperbolic manifolds are proven to minimize volume over all compact Alexandrov spaces with curvature bounded below by -1 in the same homotopy class. A version of the Besson¿Courtois¿Gallot theorem is proven for n-manifolds with boundary. The proofs extend the techniques of Besson¿Courtois¿Gallot.