The Minkowski Formula and the Quasi-Local Mass

Po-Ning Chen Mu-Tao Wang Shing-Tung Yau

Differential Geometry mathscidoc:1912.43711

Annales Henri Poincar, 20, (3), 889-904
In this article, we estimate the quasi-local energy with reference to the Minkowski spacetime (Wang and Yau in Phys Rev Lett 102 (2): 021101, 2009; Commun Math Phys 288 (3): 919942, 2009), the anti-de Sitter spacetime (Chen et al. in Commun Anal Geom, 2016. arXiv: 1603.02975), or the Schwarzschild spacetime (Chen et al. in Adv Theor Math Phys 22 (1): 123, 2018). In each case, the reference spacetime admits a conformal KillingYano 2-form which facilitates the application of the Minkowski formula in Wang et al.(J Differ Geom 105 (2): 249290, 2017) to estimate the quasi-local energy. As a consequence of the positive mass theorems in Liu and Yau (J Am Math Soc 19 (1): 181204, 2006) and Shi and Tam (Class Quantum Gravity 24 (9): 23572366, 2007) and the above estimate, we obtain rigidity theorems which characterize the Minkowski spacetime and the hyperbolic space.
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  title={The Minkowski Formula and the Quasi-Local Mass},
  author={Po-Ning Chen, Mu-Tao Wang, and Shing-Tung Yau},
  booktitle={Annales Henri Poincar},
Po-Ning Chen, Mu-Tao Wang, and Shing-Tung Yau. The Minkowski Formula and the Quasi-Local Mass. Vol. 20. In Annales Henri Poincar. pp.889-904.
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