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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.
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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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Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces
On area-constrained critical surfaces of the Hawking functional, zero Hawking energy implies the enclosed region is flat or the reference space form, but the dynamical statement is conditional on a restrictive technic...
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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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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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On the ADM mass of critical area-normalized capacitors
For asymptotically flat manifolds whose boundary capacity potential satisfies an overdetermined condition, the ADM mass is bounded below by a capacity term, with equality characterizing Schwarzschild exteriors.
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