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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The ADM mass of asymptotically flat hypersurfaces


Authors: Levi Lopes de Lima and Frederico Girão
Journal: Trans. Amer. Math. Soc. 367 (2015), 6247-6266
MSC (2010): Primary 53C21; Secondary 53C80
DOI: https://doi.org/10.1090/S0002-9947-2014-05902-3
Published electronically: October 3, 2014
MathSciNet review: 3356936
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Abstract: We provide integral formulae for the ADM mass of asymptotically flat hypersurfaces in Riemannian manifolds with a certain warped product structure in a neighborhood of `spatial' infinity, thus extending Lam's recent results on Euclidean graphs to this broader context. As applications we exhibit, in any dimension, new examples of manifolds for which versions of the Positive Mass and Riemannian Penrose inequalities hold and discuss a notion of quasi-local mass in this setting. The proof explores a novel connection between the co-vector defining the ADM mass of a hypersurface as above and the Newton tensor associated to its shape operator, which takes place in the presence of an ambient Killing field.


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Levi Lopes de Lima
Affiliation: Department of Mathematics, Federal University of Ceará, Campus do Pici, Av. Humberto Monte, s/n, 60455-760, Fortaleza/CE, Brazil
Email: levi@mat.ufc.br

Frederico Girão
Affiliation: Department of Mathematics, Federal University of Ceará, Campus do Pici, Av. Humberto Monte, s/n, 60455-760, Fortaleza/CE, Brazil
Email: fred@mat.ufc.br

DOI: https://doi.org/10.1090/S0002-9947-2014-05902-3
Received by editor(s): March 10, 2012
Received by editor(s) in revised form: June 8, 2013
Published electronically: October 3, 2014
Additional Notes: This work was partially supported by CNPq/BR and FUNCAP/CE
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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