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Mathematics > Differential Geometry

arXiv:1804.08216 (math)
[Submitted on 23 Apr 2018]

Title:The Minkowski formula and the quasi-local mass

Authors: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.
Comments: 15 pages
Subjects: Differential Geometry (math.DG)
Cite as: arXiv:1804.08216 [math.DG]
  (or arXiv:1804.08216v1 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.1804.08216
Related DOI: https://doi.org/10.1007/s00023-019-00766-7

Submission history

From: Po-Ning Chen [view email]
[v1] Mon, 23 Apr 2018 01:45:52 UTC (10 KB)
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