Constant mean curvature surfaces in warped product manifolds

S. Brendle

Constant mean curvature surfaces in warped product manifolds

Differential Geometry 2012-10-23 v4 Mathematical Physics Analysis of PDEs math.MP

Authors: S. Brendle

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.

Keywords

constant mean curvature warped product manifolds umbilic surfaces Alexandrov theorem deSitter-Schwarzschild manifold Reissner-Nordstrom manifold

Cite

@article{arxiv.1105.4273,
  title  = {Constant mean curvature surfaces in warped product manifolds},
  author = {S. Brendle},
  journal= {arXiv preprint arXiv:1105.4273},
  year   = {2012}
}

Comments

Final version, to appear in Publ Math IHES

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