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

Understand

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 $M_{\rm geod}$ the unique structure with minimum convex core volume.