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
Positive mass theor em for asymptotically flat manifolds with isolated conical singularities
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A Llarull-type rigidity result for scalar curvature holds on odd-dimensional Riemannian spin manifolds with cone-like singularities via twisted Dirac operators and spectral flow.
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.
citing papers explorer
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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
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Lipschitz rigidity for scalar curvature on singular manifolds in odd dimensions
A Llarull-type rigidity result for scalar curvature holds on odd-dimensional Riemannian spin manifolds with cone-like singularities via twisted Dirac operators and spectral flow.
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Scalar curvature rigidity of spheres with subsets removed and $L^\infty$ metrics
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.