The Weil-Petersson gradient flow of renormalized volume uniformizes relatively acylindrical manifolds
We consider the Weil-Petersson gradient vector field of renormalized volume on the deformation space of convex cocompact hyperbolic structures of a (relatively) acylindrical manifold. Using a toy model for the flow, we show that the flow has a global attracting fixed point at the structure Mgeod the unique structure with totally geodesic convex core boundary. This is joint work with Kenneth Bromberg and Franco Vargas Pallete.