A continuous Positive Mass Theorem for perturbations of Euclidean space

Abstract

We prove a Positive Mass Theorem for $C^0$-asymptotically flat Riemannian metrics with nonnegative scalar curvature in a weak sense that are sufficiently uniformly close to Euclidean space. More precisely, we show that a $C^0$-asymptotically flat Riemannian metric that is a $C^0$ perturbation of Euclidean space with nonnegative scalar curvature in the sense of Ricci flow has nonnegative mass, where the mass is given by a $C^0$ analog of the classical ADM mass previously introduced by the author.

40 pages