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arXiv:1105.4273 [math.DG]AbstractReferencesReviewsResources

Constant mean curvature surfaces in warped product manifolds

S. Brendle

Published 2011-05-21, updated 2012-10-20Version 4

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 deSitter-Schwarzschild and Reissner-Nordstrom manifolds.

Comments: Final version, to appear in Publ Math IHES
Categories: math.DG, math-ph, math.AP, math.MP
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