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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Limit of quasilocal mass integrals in asymptotically hyperbolic manifolds


Authors: Kwok-Kun Kwong and Luen-Fai Tam
Journal: Proc. Amer. Math. Soc. 141 (2013), 313-324
MSC (2010): Primary 53C20; Secondary 83C99
Published electronically: May 3, 2012
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Abstract: In this paper, we will show that the limit of some quasilocal mass integrals of the coordinate spheres in an asymptotically hyperbolic (AH) manifold is the mass integral of the AH manifold. This is the analogue of the well-known result that the limit of the Brown-York mass of coordinate spheres is the ADM mass in an asymptotically flat manifold.


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Additional Information

Kwok-Kun Kwong
Affiliation: The Institute of Mathematical Sciences and Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, People’s Republic of China
Address at time of publication: School of Mathematical Sciences, Monash University, Victoria 3800, Australia
Email: kkkwong@math.cuhk.edu.hk, kwok-kun.kwong@monash.edu

Luen-Fai Tam
Affiliation: The Institute of Mathematical Sciences and Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, People’s Republic of China
Email: lftam@math.cuhk.edu.hk

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11294-8
PII: S 0002-9939(2012)11294-8
Keywords: Quasilocal mass integral, asymptotically hyperbolic manifolds, isometric embedding.
Received by editor(s): March 9, 2011
Received by editor(s) in revised form: June 7, 2011
Published electronically: May 3, 2012
Additional Notes: This research was partially supported by Hong Kong RGC General Research Fund #CUHK 403108.
Communicated by: Jianguo Cao
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.