The mass of an asymptotically flat manifold

1986/09/01 by Robert Bartnik · 42 citations
Mathematics · #Geometric Analysis and Curvature Flows #Spectral Theory in Mathematical Physics #Nonlinear Partial Differential Equations

paper · doi:10.1002/cpa.3160390505

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.

Citations

• Properties of solutions of ordinary differential equations in banach space
• A new proof of the positive energy theorem

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