The mass of an asymptotically flat manifold

Abstract

Abstract We show that the mass of an asymptotically flat n ‐manifold is a geometric invariant. The proof is based on harmonic coordinates and, to develop a suitable existence theory, results about elliptic operators with rough coefficients on weighted Sobolev spaces are summarised. Some relations between the mass, scalar curvature and harmonic maps are described and the positive mass theorem for n ‐dimensional spin manifolds is proved.