Some lower estimates of ADM mass and Brown-York mass

TL;DR

This paper provides new lower bounds for the ADM and Brown-York masses of certain Riemannian manifolds without requiring nonnegative scalar curvature, extending previous results in geometric analysis.

Contribution

It introduces novel lower estimates for ADM and Brown-York masses under relaxed curvature conditions, broadening the understanding of mass in geometric contexts.

Findings

Lower bounds for ADM mass without nonnegative scalar curvature

Sufficient conditions for nonnegative ADM mass

Generalizations of previous Brown-York mass results

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.