On compact $3$-manifolds with nonnegative scalar curvature with a CMC boundary component
On compact $3$-manifolds with nonnegative scalar curvature with a CMC boundary component
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DOI：
10.1090/tran/7500
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发表时间：
2016-10
期刊：
影响因子：
--
通讯作者：
P. Miao;Naqing Xie
中科院分区：
文献类型：
--
作者：
P. Miao;Naqing Xie
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 \cite{M-S}.
