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

 

On the uniqueness of the foliation of spheres of constant mean curvature in asymptotically flat 3-manifolds


Authors: Jie Qing and Gang Tian
Journal: J. Amer. Math. Soc. 20 (2007), 1091-1110
MSC (2000): Primary 53C20; Secondary 58E20, 83C99
Published electronically: March 9, 2007
MathSciNet review: 2328717
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Abstract: In this note we study constant mean curvature surfaces in asymptotically flat 3-manifolds. We prove that, outside a given compact subset in an asymptotically flat 3-manifold with positive mass, stable spheres of given constant mean curvature are unique. Therefore we are able to conclude that the foliation of stable spheres of constant mean curvature in an asymptotically flat 3-manifold with positive mass outside a given compact subset is unique.


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Additional Information

Jie Qing
Affiliation: Department of Mathematics, University of California, Santa Cruz, Santa Cruz, California 95064
Email: qing@ucsc.edu

Gang Tian
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Email: tian@math.princeton.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-07-00560-7
PII: S 0894-0347(07)00560-7
Keywords: Asymptotically flat 3-manifold, stable sphere of constant mean curvature, uniqueness, center of mass, asymptotic analysis
Received by editor(s): September 24, 2005
Published electronically: March 9, 2007
Additional Notes: The first author was partially supported by DMS 0402294
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.