The Riemannian Penrose inequality is proven in arbitrary dimensions for smooth complete asymptotically flat manifolds with nonnegative scalar curvature and compact outer-minimizing minimal boundary allowing singular sets of Hausdorff dimension at most n-8, with equality only for Riemannian Schwarzs
A proof for the Riemannian positive mass theorem up to dimension 19
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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.
The positive mass theorem holds for complete asymptotically hyperbolic manifolds satisfying the dominant energy condition, including those with arbitrary ends.
Proves the spacetime positive mass theorem for asymptotically flat and asymptotically hyperboloidal initial data sets in arbitrary dimensions using Brendle-Wang's Riemannian positive mass theorem.
citing papers explorer
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Riemannian Penrose inequality in all dimensions
The Riemannian Penrose inequality is proven in arbitrary dimensions for smooth complete asymptotically flat manifolds with nonnegative scalar curvature and compact outer-minimizing minimal boundary allowing singular sets of Hausdorff dimension at most n-8, with equality only for Riemannian Schwarzs
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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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Positive mass theorem for initial data sets with arbitrary ends
The positive mass theorem holds for complete asymptotically hyperbolic manifolds satisfying the dominant energy condition, including those with arbitrary ends.
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The Hyperboloidal and Spacetime Positive Mass Theorem in All Dimensions
Proves the spacetime positive mass theorem for asymptotically flat and asymptotically hyperboloidal initial data sets in arbitrary dimensions using Brendle-Wang's Riemannian positive mass theorem.