ADM mass is nonnegative (and zero only for Euclidean space under a slightly stronger dimension bound) for complete AF L∞ metrics with nonnegative scalar curvature outside a singular set of Minkowski dimension < n−3+2/n.
Lohkamp,The higher dimensional positive mass theorem II
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abstract
We derive the Space-Time Positive Mass theorem in arbitrary dimensions, without topological constraints. The main new tools are skin structures and surgeries on minimal and marginally outer trapped hypersurfaces.
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math.DG 2years
2026 2representative citing papers
The spacetime positive energy theorem in dimensions n ≥ 4 is obtained by reducing it to the Riemannian positive mass theorem using the Jang equation with a capillary term.
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Riemannian Positive Mass Theorem in All Dimensions in the Presence of Low-Codimension Singularities
ADM mass is nonnegative (and zero only for Euclidean space under a slightly stronger dimension bound) for complete AF L∞ metrics with nonnegative scalar curvature outside a singular set of Minkowski dimension < n−3+2/n.
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On the spacetime positive energy theorem in arbitrary dimension
The spacetime positive energy theorem in dimensions n ≥ 4 is obtained by reducing it to the Riemannian positive mass theorem using the Jang equation with a capillary term.