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arXiv · 1610.07513

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

Pengzi Miao·Naqing Xie
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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 \cite{M-S}.

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Pengzi Miao, Naqing Xie. 2016-10-24. On compact $3$-manifolds with nonnegative scalar curvature with a CMC boundary component. https://arxiv.org/abs/1610.07513

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