Critical Points of Wang-Yau Quasi-Local Energy

Pengzi Miao, Luen Fai Tam, Naqing Xie

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


In this paper, we prove the following theorem regarding the Wang-Yau quasi-local energy of a spacelike two-surface in a spacetime: Let Σ be a boundary component of some compact, time-symmetric, spacelike hypersurface Ω in a time-oriented spacetime N satisfying the dominant energy condition. Suppose the induced metric on Σ has positive Gaussian curvature and all boundary components of Ω have positive mean curvature. Suppose H ≤ H0 where H is the mean curvature of Σ in Ω and H0 is the mean curvature of Σ when isometrically embedded in ℝ3. If Ω is not isometric to a domain in ℝ3, then the Brown-York mass of Σ in Ω is a strict local minimum of the Wang-Yau quasi-local energy of Σ.on a small perturbation of Σ in N, there exists a critical point of the Wang-Yau quasi-local energy of.

Original languageEnglish (US)
Pages (from-to)987-1017
Number of pages31
JournalAnnales Henri Poincare
Issue number5
StatePublished - Jul 2011

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics


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