Capacity inequalities and rigidity of cornered/conical manifolds

2017/04/14 by Cruz, C. Tiarlos
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1704.04306

Abstract

We prove capacity inequalities involving the total mean curvature of hypersurfaces with boundary in convex cones and the mass of asymptotically flat manifolds with non-compact boundary. We then give the analogous of Pölia-Szegö, Alexandrov-Fenchel and Penrose type inequalities in this setting. Among the techniques used in this paper are the inverse mean curvature flow for hypersurfaces with boundary.

Related

• ADM mass, area and capacity in asymptotically flat 3-manifolds with nonnegative scalar curvature
• The Riemannian Penrose inequality for asymptotically flat manifolds with non-compact boundary
• Functional inequalities on manifolds with non-convex boundary
• Sharp upper bounds for the capacity in the hyperbolic and Euclidean spaces
• Estimates of p-capacity for manifolds with Ricci curvature bounded from below