The mass of an asymptotically flat manifold

1986/09/01 by Robert Bartnik · 708 citations
Mathematics · #Center manifold #Curvature #Geometric Analysis and Curvature Flows #Geometry #Invariant (physics) #Invariant manifold #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Partial Differential Equations #Pure mathematics #Scalar (mathematics) #Scalar curvature #Sobolev space #Spectral Theory in Mathematical Physics

paper · doi:10.1002/cpa.3160390505

published in Communications on Pure and Applied Mathematics 39(5), 661-693 (Wiley)

openalex publication_date 1986/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/26

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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