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

Abstract

We consider the Weil-Petersson gradient vector field of renormalized volume on the deformation space of convex cocompact hyperbolic structures on (relatively) acylindrical manifolds. In this paper we prove the conjecture that the flow has a global attracting fixed point at the structure $M_{\mathrm{geod}}$ the unique structure with minimum convex core volume.

36 pages, 7 figures. Comments are welcome!