Constant positive 2-mean curvature hypersurfaces
type: Item
instance of: scholarly article
title: Constant positive 2-mean curvature hypersurfaces
zbMATH Open document ID: 1019.53028
author: Maria Fernanada Elbert
published in: Illinois Journal of Mathematics
publication date: 2003-01-01T00:00:00Z
review text: Hypersurfaces of constant 2-mean curvature in spaces of constant sectional curvature are known to be solutions to a variational problem. The author of the present paper extends this characterization to ambient spaces which are Einstein. Next, the 2-mean curvature of certain hypersurfaces in Einstein manifolds, is estimated. A consequence of the estimation 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.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 1839945
zbMATH Keywords: Einstein manifold
zbMATH Keywords: polynomial growth of volume
zbMATH Keywords: index of a hypersurface
zbMATH Keywords: 2-mean curvature
reviewed by: T. Koufogiorgos
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1839945