Quasi-local mass functionals and generalized inverse mean curvature flow (Q947302)

The inverse mean curvature flow is considered, motivated by two applications in general relativity theory, both follows the works of Hubert Bray. The first one concerns a one-parameter family of quasi-local mass functionals, which are monotone with respect to inverse mean curvature flow, that implies the estimations for AMD mass. The second one comes from the study of negative point mass singularities. The author shows that weak solutions exist for a wide class of flows. Particulary, a Penrose-type inequality for connected surfaces is an corollary.