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
DOI:
https://doi.org/10.1090/S0894-0347-07-00560-7
Published electronically:
March 9, 2007
MathSciNet review:
2328717
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
MR Author ID:
268101
Email:
qing@ucsc.edu
Gang Tian
Affiliation:
Department of Mathematics, Princeton University, Princeton, New Jersey 08544
MR Author ID:
220655
Email:
tian@math.princeton.edu
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.
