Isoperimetric interpretation for the renormalized volume of convex co-compact hyperbolic 3-manifolds

2021/05/24 by Pallete, Franco Vargas, Viana, Celso
#Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2105.11540

Abstract

We reinterpret the renormalized volume as the asymptotic difference of the isoperimetric profiles for convex co-compact hyperbolic 3-manifolds. By similar techniques we also prove a sharp Minkowski inequality for horospherically convex sets in ℍ³. Finally, we include the classification of stable constant mean curvature surfaces in regions bounded by two geodesic planes in ℍ³ or in cyclic quotients of ℍ³.

Related

• Exhaustion of isoperimetric regions in asymptotically hyperbolic manifolds with scalar curvature R≥ -6
• Volume functions and boundary data of 3-dimensional hyperbolic manifolds
• Large isoperimetric surfaces in initial data sets
• Minkowski inequality in Cartan-Hadamard manifolds
• Isoperimetric Bounds on Convex Manifolds