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

DOI:
https://doi.org/10.1090/S0002-9939-2012-11294-8

Published electronically:
May 3, 2012

MathSciNet review:
2988733

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-2012-11294-8

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.