On compact 3-manifolds with nonnegative scalar curvature with a CMC boundary component

Miao, Pengzi; Xie, Naqing

doi:10.1090/tran/7500

On compact $3$-manifolds with nonnegative scalar curvature with a CMC boundary component
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by Pengzi Miao and Naqing Xie PDF

Trans. Amer. Math. Soc. 370 (2018), 5887-5906 Request permission

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.

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