Stable hypersurfaces with zero scalar curvature in Euclidean space
Differential Geometry
2017-04-13 v2
Abstract
In this paper we prove some results concerning stability of hypersurfaces in the four dimensional Euclidean space with zero scalar curvature. First we prove there is no complete stable hypersurface with zero scalar curvature, polynomial growth of integral of the mean curvature, and with the Gauss-Kronecker curvature bounded away from zero. We conclude this paper giving a sufficient condition for a regular domain to be stable in terms of the mean and the Gauss-Kronecker curvatures of the hypersurface and the radius of the smallest extrinsic ball which contains the domain.
Keywords
Cite
@article{arxiv.1510.03741,
title = {Stable hypersurfaces with zero scalar curvature in Euclidean space},
author = {Hilário Alencar and Manfredo do Carmo and Gregório Silva Neto},
journal= {arXiv preprint arXiv:1510.03741},
year = {2017}
}
Comments
7 pages. Accepted for publication at the Arkiv f\"or Matematik