Convergence of the gradient flow of renormalized volume to convex cores with totally geodesic boundary

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 M_geod the unique structure with totally geodesic convex core boundary.

This is joint work with Kenneth Bromberg, and Franco Vargas Pallete