Riemannian Penrose inequality in all dimensions
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913080718393344 |
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| author | Bi, Yuchen Zhu, Jintian |
| author_facet | Bi, Yuchen Zhu, Jintian |
| contents | We prove the Riemannian Penrose inequality in arbitrary dimension for smooth complete asymptotically flat manifolds with nonnegative scalar curvature and compact outer-minimizing minimal boundary, where the boundary is allowed to have a singular set of Hausdorff dimension at most \(n-8\). Moreover, the equality holds exactly when the manifold is isometric to the Riemannian Schwarzschild exteriors. Our proof extends Bray's conformal-flow method to higher dimensions, where the outer-minimizing enclosures along the flow may be singular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00680 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Riemannian Penrose inequality in all dimensions Bi, Yuchen Zhu, Jintian Differential Geometry We prove the Riemannian Penrose inequality in arbitrary dimension for smooth complete asymptotically flat manifolds with nonnegative scalar curvature and compact outer-minimizing minimal boundary, where the boundary is allowed to have a singular set of Hausdorff dimension at most \(n-8\). Moreover, the equality holds exactly when the manifold is isometric to the Riemannian Schwarzschild exteriors. Our proof extends Bray's conformal-flow method to higher dimensions, where the outer-minimizing enclosures along the flow may be singular. |
| title | Riemannian Penrose inequality in all dimensions |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2605.00680 |