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On the uniqueness of the foliation of spheres of constant mean curvature in asymptotically flat 3-manifolds
Author(s):
Jie
Qing;
Gang
Tian
Journal:
J. Amer. Math. Soc.
20
(2007),
1091-1110.
MSC (2000):
Primary 53C20;
Secondary 58E20, 83C99
Posted:
March 9, 2007
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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:
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
Posted:
March 9, 2007
Additional Notes:
The first author was partially supported by DMS 0402294
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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