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

Pengzi Miao, Naqing Xie

Research output: Contribution to journalArticle

5 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)5887-5906
Number of pages20
JournalTransactions of the American Mathematical Society
Volume370
Issue number8
DOIs
StatePublished - Jan 1 2018

Keywords

  • CMC surfaces
  • Riemannian penrose inequality
  • Scalar curvature

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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