Abstract
Hypersurfaces of constant $2$-mean curvature in spaces of constant sectional curvature are known to be solutions to a variational problem. We extend this characterization to ambient spaces which are Einstein. We then estimate the $2$-mean curvature of certain hypersurfaces in Einstein manifolds. A consequence of our estimates is a generalization of a result, first proved by Chern, showing that there are no complete graphs in the Euclidean space with positive constant $2$-mean curvature.
Citation
Maria Fernanda Elbert. "Constant positive 2-mean curvature hypersurfaces." Illinois J. Math. 46 (1) 247 - 267, Spring 2002. https://doi.org/10.1215/ijm/1258136153
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