### 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 ≤ H_{0} where H is the mean curvature of Σ in Ω and H_{0} is the mean curvature of Σ when isometrically embedded in ℝ^{3}. If Ω is not isometric to a domain in ℝ^{3}, 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 language | English (US) |
---|---|

Pages (from-to) | 987-1017 |

Number of pages | 31 |

Journal | Annales Henri Poincare |

Volume | 12 |

Issue number | 5 |

DOIs | |

State | Published - Jul 2011 |

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### ASJC Scopus subject areas

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

### Cite this

*Annales Henri Poincare*,

*12*(5), 987-1017. https://doi.org/10.1007/s00023-011-0097-0

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

Research output: Contribution to journal › Article

*Annales Henri Poincare*, vol. 12, no. 5, pp. 987-1017. https://doi.org/10.1007/s00023-011-0097-0

}

TY - JOUR

T1 - Critical Points of Wang-Yau Quasi-Local Energy

AU - Miao, Pengzi

AU - Tam, Luen Fai

AU - Xie, Naqing

PY - 2011/7

Y1 - 2011/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79956136887&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79956136887&partnerID=8YFLogxK

U2 - 10.1007/s00023-011-0097-0

DO - 10.1007/s00023-011-0097-0

M3 - Article

VL - 12

SP - 987

EP - 1017

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 1424-0637

IS - 5

ER -