Proves Riemannian positive mass theorem for asymptotically flat L^∞ metrics with subcritical singular sets of Minkowski dimension less than n-3 + 2/n (rigidity for ≤ n-3 + 1/(n-1)), using density theorem, capacity estimates, conformal blow-up, and μ-bubble descent.
Positive scalar curvature with point singularities
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Asymptotically flat L^∞ ∩ W^{1,n} manifolds with non-negative distributional scalar curvature satisfy the positive mass theorem, with zero mass implying global isometry to Euclidean space via an integral distance.
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
Proves scalar curvature rigidity for L^∞ metrics on S^n minus high-codimension subsets with wrapping property, plus analogous result for tori and positive mass theorem corollary for L^∞ AF spin manifolds.
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Riemannian Positive Mass Theorem in All Dimensions in the Presence of Low-Codimension Singularities
Proves Riemannian positive mass theorem for asymptotically flat L^∞ metrics with subcritical singular sets of Minkowski dimension less than n-3 + 2/n (rigidity for ≤ n-3 + 1/(n-1)), using density theorem, capacity estimates, conformal blow-up, and μ-bubble descent.
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Spaces with distributional scalar curvature bounded from below: Optimal regularity and positive mass
Asymptotically flat L^∞ ∩ W^{1,n} manifolds with non-negative distributional scalar curvature satisfy the positive mass theorem, with zero mass implying global isometry to Euclidean space via an integral distance.
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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