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.
Singular metrics with nonnegative scalar curvature and rcd
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Under a non-surjectivity assumption on the fundamental group homomorphism from the singular set, an L^∞ metric on a torus with non-negative scalar curvature outside a Minkowski dimension ≤ n-3+(n-1)^{-1} singular set extends to a smooth flat metric, proved via weighted scalar curvature and the relat
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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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$L^\infty$-metrics on tori and Schoen's conjecture
Under a non-surjectivity assumption on the fundamental group homomorphism from the singular set, an L^∞ metric on a torus with non-negative scalar curvature outside a Minkowski dimension ≤ n-3+(n-1)^{-1} singular set extends to a smooth flat metric, proved via weighted scalar curvature and the relat