Stability of the Riemannian positive mass theorem for spin manifolds

Abstract

We extend the Dong-Song stability theorem for the Riemannian positive mass theorem to higher dimensional spin manifolds. More precisely, for a sequence of complete asymptotically flat spin n-manifolds with nonnegative scalar curvature and ADM masses tending to zero, the exterior regions obtained by excising domains whose boundary areas tend to zero converge to Euclidean space in the pointed measured Gromov-Hausdorff topology. The proof constructs coordinates from globally minimal graphs and controls the metric defect by spinors.