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 mathbb R3{mathbb R^3} . If Ω is not isometric to a domain in mathbb R3{mathbb R^3}, then 1. the Brown–York mass of Σ in Ω is a strict local minimum of the Wang–Yau quasi-local energy of Σ.
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机译：在本文中，我们证明了关于时空的两面空间的Wang-Yau准局部能量的以下定理：设Σ为时间定向的某些紧致，时间对称，空间状超表面Ω的边界分量满足主导能量条件的时空N。假定Σ上的感应度量具有正高斯曲率，而Ω的所有边界分量均具有正平均曲率。假设H≤H 0 ，其中H是等距嵌入Mathbb R 3 中的Σ的平均曲率，H 0 是Σ的平均曲率。 sup> {mathbb R ^ 3}。如果Ω与mathbb R 3 {mathbb R ^ 3}中的域不是等距的，则1.Ω中Σ的布朗-约克质量是Wang-Yau准方程的严格局部最小值。 Σ的局部能量。
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