Isoperimetry, scalar curvature, and mass in asymptotically flat Riemannian $3$-manifolds

Abstract

Let $(M,g)$ be an asymptotically flat Riemannian $3$-manifold with non-negative scalar curvature and positive mass. We show that each leaf of the canonical foliation through stable constant mean curvature surfaces of the end of $(M,g)$ is uniquely isoperimetric for the volume it encloses.

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