Total Mean Curvature, Scalar Curvature, and a Variational Analog of Brown–York Mass

Christos Mantoulidis, Pengzi Miao

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

We study the supremum of the total mean curvature on the boundary of compact, mean-convex 3-manifolds with nonnegative scalar curvature, and a prescribed boundary metric. We establish an additivity property for this supremum and exhibit rigidity for maximizers assuming the supremum is attained. When the boundary consists of 2-spheres, we demonstrate that the finiteness of the supremum follows from the previous work of Shi–Tam and Wang–Yau on the quasi-local mass problem in general relativity. In turn, we define a variational analog of Brown–York quasi-local mass without assuming that the boundary 2-sphere has positive Gauss curvature.

Original languageEnglish (US)
Pages (from-to)1-16
Number of pages16
JournalCommunications in Mathematical Physics
DOIs
StateAccepted/In press - Oct 14 2016

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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