A generalization of Liu-Yau's quasi-local mass
A generalization of Liu-Yau's quasi-local mass
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DOI：
10.4310/cag.2007.v15.n2.a2
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发表时间：
2006-02
影响因子：
0.7
通讯作者：
Mu-Tao Wang;S. Yau
中科院分区：
文献类型：
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作者：
Mu-Tao Wang;S. Yau
Liu和第二作者在[LY， LY2]中提出了准局部质量的定义，并证明了其正性。这是通过一个不等式来证明的，这个不等式反过来可以解释为高斯正曲率曲面的等距嵌入的总平均曲率比较定理。黎曼版本对应于Shi和Tam [ST]的早期定理。在本文中，我们将这个不等式推广到允许曲面高斯曲率为负的情况。这是通过在闵可夫斯基空间的双曲面中进行等距嵌入来实现的，并获得了一个面向未来的类时准局部能量动量。
In [LY, LY2], Liu and the second author propose a definition of the quasi-local mass and prove its positivity. This is demonstrated through an inequality which in turn can be interpreted as a total mean curvature comparison theorem for isometric embeddings of a surface of positive Gaussian curvature. The Riemannian version corresponds to an earlier theorem of Shi and Tam [ST]. In this article, we generalize such an inequality to the case when the Gaussian curvature of the surface is allowed to be negative. This is done by an isometric embedding into the hyperboloid in the Minkowski space and a future-directed time-like quasi-local energy-momentum is obtained.