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On the rigidity of Riemannian–Penrose inequality for asymptotically flat 3-manifolds with corners

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Abstract

In this paper we prove a rigidity result for the equality case of the Penrose inequality on 3-dimensional asymptotically flat manifolds with nonnegative scalar curvature and corners. Our result also has deep connections with the equality cases of Theorem 1 in Miao (Commun Math Phys 292(1):271–284, 2009) and Theorem 1.1 in Lu and Miao (Minimal hypersurfaces and boundary behavior of compact manifolds with nonnegative scalar curvature, arXiv:1703.08164v2, 2017).

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Authors and Affiliations

  1. Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China

    Yuguang Shi & Wenlong Wang

  2. Department of Mathematics, Hangzhou Normal University, Hangzhou, 310012, People’s Republic of China

    Haobin Yu

Authors
  1. Yuguang Shi
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  2. Wenlong Wang
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  3. Haobin Yu
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Corresponding author

Correspondence to Yuguang Shi.

Additional information

Y. Shi and H. Yu: Research partially supported by NSFC 11671015 and NSFC 11731001.

W. Wang: Research partially supported by National Postdoctoral Program for Innovative Talents of China 201700007 and NSFC 11701326.

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Shi, Y., Wang, W. & Yu, H. On the rigidity of Riemannian–Penrose inequality for asymptotically flat 3-manifolds with corners. Math. Z. 291, 569–589 (2019). https://doi.org/10.1007/s00209-018-2095-0

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  • DOI: https://doi.org/10.1007/s00209-018-2095-0

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