Some lower estimates of ADM mass and Brown-York mass

2004/06/28 by Yuguang Shi, Shi, Yuguang, Luen-fai Tam +1
Mathematics · Physics and Astronomy · #53C20 (Primary) #83C40 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP #msc:53C20 #msc:83C40

paper · pdf · doi:10.48550/arxiv.math/0406559

arxiv created 2004/07/01 · arxiv updated 2009/12/01

Abstract

We give some lower estimates of the ADM mass of an asymptotically flat (AF) Riemannian manifold without assuming that the scalar curvature of the manifold is nonnegative. Some sufficient conditions for an AF manifold to have nonnegative ADM mass are obtained. We also give some lower estimates of the Brown-York mass of a compact three manifold with smooth boundary. From these estimates, we generalize some previous results of the authors.

Related

• Mass Lower Bounds for Asymptotically Locally Flat Manifolds
• The ADM mass of asymptotically flat hypersurfaces
• Mass of asymptotically flat 3-manifolds with boundary
• Curvature Estimates and the Positive Mass Theorem
• Large-sphere and small-sphere limits of the Brown-York mass