Minimizing properties of critical points of quasi-local energy

Po-Ning Chen Columbia University Mu-Tao Wang Columbia University Shing-Tung Yau Harvard University

Differential Geometry mathscidoc:1608.10024

Communications in Mathematical Physics, 329, (3), 919–935, 2014.8
In relativity, the energy of a moving particle depends on the observer, and the rest mass is the minimal energy seen among all observers. The Wang–Yau quasi-local mass for a surface in spacetime introduced in Wang and Yau (Phys Rev Lett 102(2):021101, 2009 ; Commun Math Phys 288(3):919–942, 2009) is defined by minimizing quasi-local energy associated with admissible isometric embeddings of the surface into the Minkowski space. A critical point of the quasi-local energy is an isometric embedding satisfying the Euler–Lagrange equation. In this article, we prove results regarding both local and global minimizing properties of critical points of the Wang–Yau quasi-local energy. In particular, under a condition on the mean curvature vector we show a critical point minimizes the quasi-local energy locally. The same condition also implies that the critical point is globally minimizing among all axially symmetric embedding provided the image of the associated isometric embedding lies in a totally geodesic Euclidean 3-space.
quasi-local energy, Wang–Yau quasi-local mass, Minkowski space, associated isometric embedding
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  title={Minimizing properties of critical points of quasi-local energy},
  author={Po-Ning Chen, Mu-Tao Wang, and Shing-Tung Yau},
  booktitle={Communications in Mathematical Physics},
Po-Ning Chen, Mu-Tao Wang, and Shing-Tung Yau. Minimizing properties of critical points of quasi-local energy. 2014. Vol. 329. In Communications in Mathematical Physics. pp.919–935.
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