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PreprintarXiv licencearXiv

Riemannian Penrose inequality in all dimensions

  • Yuchen Bi
  • Jintian Zhu
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@misc{bi2026riemannian,
  title = {{Riemannian Penrose inequality in all dimensions}},
  author = {Yuchen Bi and Jintian Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.00680},
  eprint = {2605.00680},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.00680},
}
RIS
TY  - UNPB
TI  - Riemannian Penrose inequality in all dimensions
AU  - Yuchen Bi
AU  - Jintian Zhu
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2605.00680
UR  - https://arxiv.org/abs/2605.00680
AB  - 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.
ER  -