Critical Points of Wang–Yau Quasi-Local Energy
Critical Points of Wang–Yau Quasi-Local Energy
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DOI：
10.1007/s00023-011-0097-0
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发表时间：
2010-03
期刊：
影响因子：
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通讯作者：
P. Miao;Luen-Fai Tam;Naqing Xie
中科院分区：
文献类型：
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作者：
P. Miao;Luen-Fai Tam;Naqing Xie
本文证明了时空中一类类空间曲面的Wang-Yau拟局部能量的定理：设Σ是某个紧致的、时间对称的类空间超曲面Ω在面向时间的时空中满足优势能量条件的边界分量。假设Σ上的诱导度规具有正的高斯曲率，并且Ω的所有边界分量具有正的平均曲率。假想h≤ho0wherehis为Ω中Σ的平均曲率，ho0为Σ等距嵌入时的平均曲率。如果Ω与in的定义域不是等距的，则1。Ω中Σ的Brown-York质量是Σ.2的Wang-Yau准局部能量的严格局部最小值。在Σ inN的小扰动下，存在的Wang-Yau准局部能量的临界点。
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 spacetimeNsatisfying the dominant energy condition. Suppose the induced metric on Σ has positive Gaussian curvature and all boundary components of Ω have positive mean curvature. SupposeH≤H0whereHis the mean curvature of Σ in Ω andH0is the mean curvature of Σ when isometrically embedded in. If Ω is not isometric to a domain in, then1.the Brown–York mass of Σ in Ω is a strict local minimum of the Wang–Yau quasi-local energy of Σ.2.on a small perturbationof Σ inN, there exists a critical point of the Wang–Yau quasi-local energy of.