On a Penrose-Like Inequality in Dimensions Less than Eight

Abstract

On an asymptotically flat manifold |$M^n$| with nonnegative scalar curvature, with outer minimizing boundary |$\Sigma$|⁠, we prove a Penrose-like inequality in dimensions |$n < 8$|⁠, under suitable assumptions on the mean curvature and the scalar curvature of |$\Sigma$|⁠.