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The Higher Dimensional Positive Mass Theorem I
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The Higher Dimensional Positive Mass Theorem I
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We derive the Riemannian Positive Mass theorem in arbitrary dimensions, without any topological constraints. The main new tools are skin structures and surgeries on minimal hypersurfaces.
Forward citations
Cited by 5 Pith papers
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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 est...
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A dimension descent scheme for the positive mass theorem in arbitrary dimension
A new inductive dimension descent scheme extends the Schoen-Yau positive mass theorem to arbitrary dimensions using shielding principles, conformal blow-ups, and Cheeger-Naber singular set bounds.
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A conformal reduction for the X-ADM mass
Positivity of the X-ADM mass is equivalent to the standard positive mass theorem via conformal reduction, establishing the X-positive mass theorem and mass-charge inequality in all dimensions.
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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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Charged parallel spinors and applications to mass--charge inequalities
Equality in the spin mass–charge inequality holds precisely when the manifold carries a charged parallel spinor and is isometric to extremal Reissner–Nordström (connected boundary or one cylindrical end).
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