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Constant mean curvature surfaces in warped product manifolds
 Simon Brendle
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Abstract
We consider surfaces with constant mean curvature in certain warped product manifolds. We show that any such surface is umbilic, provided that the warping factor satisfies certain structure conditions. This theorem can be viewed as a generalization of the classical Alexandrov theorem in Euclidean space. In particular, our results apply to the deSitterSchwarzschild and ReissnerNordstrom manifolds.
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 Title
 Constant mean curvature surfaces in warped product manifolds
 Journal

Publications mathématiques de l'IHÉS
Volume 117, Issue 1 , pp 247269
 Cover Date
 20130601
 DOI
 10.1007/s1024001200475
 Print ISSN
 00738301
 Online ISSN
 16181913
 Publisher
 SpringerVerlag
 Additional Links
 Authors

 Simon Brendle ^{(1)}
 Author Affiliations

 1. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA