C. Tiarlos Cruz — Neckpinchhttps://neckpinch.com/authors/c-tiarlos-cruz/New arXiv papers by C. Tiarlos Cruz, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT Capacity inequalities and rigidity of cornered/conical manifoldshttps://neckpinch.com/papers/1704.04306/arxiv:1704.04306Fri, 14 Apr 2017 00:00:00 GMTC. Tiarlos Cruz — 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.Mean curvature flowOther curvature flowsInverse mean curvature flowStability & uniquenessBoundaries & non-compactGeometric inequalities