## Illinois Journal of Mathematics

### Constant positive 2-mean curvature hypersurfaces

Maria Fernanda Elbert

#### 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.

#### Article information

Source
Illinois J. Math., Volume 46, Number 1 (2002), 247-267.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258136153

Digital Object Identifier
doi:10.1215/ijm/1258136153

Mathematical Reviews number (MathSciNet)
MR1936088

Zentralblatt MATH identifier
1019.53028

#### Citation

Elbert, Maria Fernanda. Constant positive 2-mean curvature hypersurfaces. Illinois J. Math. 46 (2002), no. 1, 247--267. doi:10.1215/ijm/1258136153. https://projecteuclid.org/euclid.ijm/1258136153