Isoperimetry for asymptotically flat 3-manifolds with positive ADM mass

Abstract

Let $$(M^3, g)$$ be an asymptotically flat 3-manifold with positive ADM mass. In this paper, we show that each leaf of the canonical foliation consisting of stable constant mean curvature spheres is the unique isoperimetric surface for the volume it encloses. Our proof is based on “fill-in” argument and sharp isoperimetric inequality on asymptotically flat 3-manifold with non-negative scalar curvature.