On compact $3$-manifolds with nonnegative scalar curvature with a CMC boundary component
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- by Pengzi Miao and Naqing Xie PDF
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Abstract:
We apply the Riemannian Penrose inequality and the Riemannian positive mass theorem to derive inequalities on the boundary of a class of compact Riemannian $3$-manifolds with nonnegative scalar curvature. The boundary of such a manifold has a CMC component, i.e., a $2$-sphere with positive constant mean curvature; and the rest of the boundary, if nonempty, consists of closed minimal surfaces. A key step in our proof is the construction of a collar extension that is inspired by the method of Mantoulidis-Schoen.References
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Additional Information
- Pengzi Miao
- Affiliation: Department of Mathematics, University of Miami, Coral Gables, Florida 33146
- MR Author ID: 715810
- Email: pengzim@math.miami.edu
- Naqing Xie
- Affiliation: School of Mathematical Sciences, Fudan University, Shanghai 200433, People’s Republic of China
- MR Author ID: 770267
- ORCID: 0000-0001-5520-0542
- Email: nqxie@fudan.edu.cn
- Received by editor(s): January 30, 2017
- Published electronically: April 17, 2018
- Additional Notes: The first named author’s research was partially supported by Simons Foundation Collaboration Grant for Mathematicians #281105.
The second named author’s research was partially supported by the National Science Foundation of China #11671089, #11421061. - © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 5887-5906
- MSC (2010): Primary 53C20; Secondary 83C99
- DOI: https://doi.org/10.1090/tran/7500
- MathSciNet review: 3803150