Critical Points of Wang-Yau Quasi-Local Energy

Pengzi Miao, Luen Fai Tam, Naqing Xie

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

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
Volume12
Issue number5
DOIs
StatePublished - Jul 2011

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Critical point
critical point
Mean Curvature
curvature
Positive Curvature
Energy
Space-time
Spacelike Hypersurface
energy
Total curvature
Small Perturbations
Local Minima
Isometric
theorems
Metric
perturbation
Theorem

ASJC Scopus subject areas

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

Cite this

Critical Points of Wang-Yau Quasi-Local Energy. / Miao, Pengzi; Tam, Luen Fai; Xie, Naqing.

In: Annales Henri Poincare, Vol. 12, No. 5, 07.2011, p. 987-1017.

Research output: Contribution to journalArticle

Miao, Pengzi ; Tam, Luen Fai ; Xie, Naqing. / Critical Points of Wang-Yau Quasi-Local Energy. In: Annales Henri Poincare. 2011 ; Vol. 12, No. 5. pp. 987-1017.
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