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
Positive mass theorem on manifolds admitting corners along a hypersurface
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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.
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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.