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arXiv · 1804.08216

The Minkowski formula and the quasi-local mass

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

In this article, we estimate the quasi-local energy with reference to the Minkowski spacetime [16,17], the anti-de Sitter spacetime [4], or the Schwarzschild spacetime [3]. In each case, the reference spacetime admits a conformal Killing-Yano 2-form which facilitates the application of the Minkowski formula in [15] to estimate the quasi-local energy. As a consequence of the positive mass theorems in [9,13] and the above estimate, we obtain rigidity theorems which characterize the Minkowski spacetime and the hyperbolic space.

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Po-Ning Chen, Mu-Tao Wang, Shing-Tung Yau. 2018-04-23. The Minkowski formula and the quasi-local mass. https://doi.org/10.1007/s00023-019-00766-7

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