Convergence of the gradient flow of renormalized volume to convex cores with totally geodesic boundary. Issue 4 (4th April 2023)

• Record Type: Journal Article
• Authors: Bridgeman, Martin; Bromberg, Kenneth; Vargas Pallete, Franco
• Is Part Of: Compositio mathematica. Volume 159:Issue 4(2023)
• Page Start: 830
• Page End: 859
• Publication Date: 2023-04-04
• Subjects: renormalized volume -- Weil–Petersson metric -- hyperbolic geometry; 32G15 -- 32Q45 -- 51P05; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X2300708X
• Languages: English
• ISSNs: 0010-437X

Abstract

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