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

On the rigidity of Riemannian–Penrose inequality for asymptotically flat 3-manifolds with corners Math. Z. https://doi.org/10.1007/s00209-018-2095-0 Mathematische Zeitschrift On the rigidity of Riemannian–Penrose inequality for asymptotically flat 3-manifolds with corners 1 1 2 Yuguang Shi · Wenlong Wang · Haobin Yu Received: 9 November 2017 / Accepted: 1 April 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 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 cor- ners. 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 curva- ture, arXiv:1703.08164v2, 2017). Keywords Penrose inequality · Asymptotically flat manifold with corner · Stable CMC surfaces Mathematics Subject Classification Primary 53C20; Secondary 83C99 1 Introduction In this paper, we are interested in what happens when the equality holds in the Riemannian Penrose inequality on asymptotically flat manifolds with corners (see Theorem 1.1 below). 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

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

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
0025-5874
eISSN
1432-1823
D.O.I.
10.1007/s00209-018-2095-0
Publisher site
See Article on Publisher Site

Abstract

Math. Z. https://doi.org/10.1007/s00209-018-2095-0 Mathematische Zeitschrift On the rigidity of Riemannian–Penrose inequality for asymptotically flat 3-manifolds with corners 1 1 2 Yuguang Shi · Wenlong Wang · Haobin Yu Received: 9 November 2017 / Accepted: 1 April 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 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 cor- ners. 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 curva- ture, arXiv:1703.08164v2, 2017). Keywords Penrose inequality · Asymptotically flat manifold with corner · Stable CMC surfaces Mathematics Subject Classification Primary 53C20; Secondary 83C99 1 Introduction In this paper, we are interested in what happens when the equality holds in the Riemannian Penrose inequality on asymptotically flat manifolds with corners (see Theorem 1.1 below). 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.

Journal

Mathematische ZeitschriftSpringer Journals

Published: Jun 2, 2018

References

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