TY - JOUR

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

AU - Miao, Pengzi

AU - Tam, Luen Fai

AU - Xie, Naqing

N1 - Funding Information:
P. Miao’s research was partially supported by Australian Research Council Discovery Grant #DP0987650. L.-F. Tam’s research was partially supported by Hong Kong RGC General Research Fund #CUHK 403108. N. Xie’s research was partially supported by the National Science Foundation of China #10801036, #11011140233 and the Innovation Program of Shanghai Municipal Education Commission #11ZZ01.

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.

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U2 - 10.1007/s00023-011-0097-0

DO - 10.1007/s00023-011-0097-0

M3 - Article

AN - SCOPUS:79956136887

VL - 12

SP - 987

EP - 1017

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 1424-0637

IS - 5

ER -