On compact -manifolds with nonnegative scalar curvature with a CMC boundary component

Authors:
Pengzi Miao and Naqing Xie

Journal:
Trans. Amer. Math. Soc. **370** (2018), 5887-5906

MSC (2010):
Primary 53C20; Secondary 83C99

DOI:
https://doi.org/10.1090/tran/7500

Published electronically:
April 17, 2018

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Abstract | References | Similar Articles | Additional Information

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 -manifolds with nonnegative scalar curvature. The boundary of such a manifold has a CMC component, i.e., a -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.

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Additional Information

**Pengzi Miao**

Affiliation:
Department of Mathematics, University of Miami, Coral Gables, Florida 33146

Email:
pengzim@math.miami.edu

**Naqing Xie**

Affiliation:
School of Mathematical Sciences, Fudan University, Shanghai 200433, People’s Republic of China

Email:
nqxie@fudan.edu.cn

DOI:
https://doi.org/10.1090/tran/7500

Keywords:
Scalar curvature,
CMC surfaces,
Riemannian Penrose inequality

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.

Article copyright:
© Copyright 2018
American Mathematical Society