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
The inverse mean curvature flow and the Riemannian Penrose inequality
5 Pith papers cite this work, alongside 767 external citations. Polarity classification is still indexing.
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New unified proof of the Positive Mass Theorem and Riemannian Penrose Inequality for 3D asymptotically flat manifolds with C^{2,α} metrics up to a hypersurface, via approximate monotonicity of a potential-theoretic quantity.
Defines intrinsic Brown-York mass at infinity for hypersurfaces in 4D AF manifolds whose asymptotic expansion recovers ADM mass plus a shape-dependent correction that vanishes for nearly round surfaces under a decay condition.
Surveys Calabi-Yau literature and symmetries, characterizes isometries, introduces volume ratio formula on CICYs, and proposes symmetry-aware GNN model for Ricci-flat metrics.
Establishes monotone quantities and sharp mass-p-capacity inequalities for p-capacitary functions in 3D AF half-spaces with nonnegative scalar and boundary mean curvature, equality on Schwarzschild half-spaces.
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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Riemannian Penrose Inequality for Manifolds with Corners via Non-Linear Potential Theory
New unified proof of the Positive Mass Theorem and Riemannian Penrose Inequality for 3D asymptotically flat manifolds with C^{2,α} metrics up to a hypersurface, via approximate monotonicity of a potential-theoretic quantity.
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Intrinsic Brown--York Type Mass at Infinity in Four Dimensions
Defines intrinsic Brown-York mass at infinity for hypersurfaces in 4D AF manifolds whose asymptotic expansion recovers ADM mass plus a shape-dependent correction that vanishes for nearly round surfaces under a decay condition.
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The Sharp Edges of Calabi-Yau Manifolds: Designing Symmetric Models for Ricci-flat Metrics
Surveys Calabi-Yau literature and symmetries, characterizes isometries, introduces volume ratio formula on CICYs, and proposes symmetry-aware GNN model for Ricci-flat metrics.
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Mass-$p$-Capacity Inequalities in Asymptotically Flat Half-Spaces
Establishes monotone quantities and sharp mass-p-capacity inequalities for p-capacitary functions in 3D AF half-spaces with nonnegative scalar and boundary mean curvature, equality on Schwarzschild half-spaces.