On the Positive Mass, Penrose, an ZAS Inequalities in General Dimension

Abstract

After a detailed introduction including new examples, we give an exposition focusing on the Riemannian cases of the positive mass, Penrose, and ZAS in- equalities of general relativity, in general dimension.

arXiv commentWill appear in the book "Surveys in Geometric Analysis and Relativity celebrating Richard Schoen's 60th birthday."

References in corpus (8)

• The Dynamics of General Relativity
• The Higher Dimensional Positive Mass Theorem II
• On the stability of naked singularities
• The initial value problem for linearized gravitational perturbations of the Schwarzschild naked singularity
• Singular Minimal Hypersurfaces and Scalar Curvature
• Stability and rigidity of extremal surfaces in Riemannian geometry and General Relativity
• Zero area singularities in general relativity and inverse mean curvature flow
• Inductive Analysis on Singular Minimal Hypersurfaces

Cited by in corpus (5)

• The Gauss-Bonnet-Chern mass for graphic manifolds
• A new mass for asymptotically flat manifolds
• The equality case of the Penrose inequality for asymptotically flat graphs
• Hypersurfaces with nonnegative scalar curvature
• A positive mass theorem in the Einstein-Gauss-Bonnet theory