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Mathematische Zeitschrift

, Volume 291, Issue 1–2, pp 569–589 | Cite as

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

  • Yuguang ShiEmail author
  • Wenlong Wang
  • Haobin Yu
Article

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).

Keywords

Penrose inequality Asymptotically flat manifold with corner Stable CMC surfaces 

Mathematics Subject Classification

Primary 53C20 Secondary 83C99 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Key Laboratory of Pure and Applied Mathematics, School of Mathematical SciencesPeking UniversityBeijingPeople’s Republic of China
  2. 2.Department of MathematicsHangzhou Normal UniversityHangzhouPeople’s Republic of China

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