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Constant mean curvature surfaces in warped product manifolds

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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 deSitter-Schwarzschild and Reissner-Nordstrom manifolds.

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

    Simon Brendle

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  1. Simon Brendle
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Correspondence to Simon Brendle.

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Brendle, S. Constant mean curvature surfaces in warped product manifolds. Publ.math.IHES 117, 247–269 (2013). https://doi.org/10.1007/s10240-012-0047-5

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  • DOI: https://doi.org/10.1007/s10240-012-0047-5

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