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On the uniqueness of the foliation of spheres of constant mean curvature in asymptotically flat 3-manifolds |
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| Authors: | Jie Qing Gang Tian |
| Affiliation: | Department of Mathematics, University of California, Santa Cruz, Santa Cruz, California 95064 ; Department of Mathematics, Princeton University, Princeton, New Jersey 08544 |
| 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. |
| Keywords: | Asymptotically flat 3-manifold stable sphere of constant mean curvature uniqueness center of mass asymptotic analysis |
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