Constant mean curvature surfaces in warped product manifolds

2013/06/07 by Simon Brendle · 3 citations

paper · doi:10.1007/s10240-012-0047-5

crossref issued 2013/06/07 · crossref published 2013/06/07 · crossref published-online 2013/06/07 · crossref created 2013/11/08 · crossref deposited 2026/02/17 · crossref indexed 2026/08/02

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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