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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Positivity of quasi-local mass II


Authors: Chiu-Chu Melissa Liu and Shing-Tung Yau
Journal: J. Amer. Math. Soc. 19 (2006), 181-204
MSC (2000): Primary 83C99; Secondary 53C21, 53C27
Published electronically: July 12, 2005
MathSciNet review: 2169046
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Abstract:

We prove the following stronger version of the positivity of quasi-local energy (mass) stated by Liu and Yau: the quasi-local energy of each connected component of the boundary of a compact spacelike hypersurface which satisfies the local energy condition is strictly positive unless the spacetime is flat along the spacelike hypersurface and the boundary of the spacelike hypersurface is connected.


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Additional Information

Chiu-Chu Melissa Liu
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Address at time of publication: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
Email: ccliu@math.harvard.edu, ccliu@math.northwestern.edu

Shing-Tung Yau
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Email: yau@math.harvard.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-05-00497-2
PII: S 0894-0347(05)00497-2
Keywords: Quasi-local energy, local energy condition, positive mass theorem
Received by editor(s): January 20, 2005
Published electronically: July 12, 2005
Additional Notes: The second author is supported in part by the National Science Foundation under Grant No. DMS-0306600.
Article copyright: © Copyright 2005 by Chiu-Chu Melissa Liu and Shing-Tung Yau