Stable hypersurfaces with zero scalar curvature in Euclidean space

Hilário Alencar Instituto de Matemática, Universidade Federal de Alagoas Manfredo do Carmo Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, RJ, Brazil Gregório Silva Neto Instituto de Matemática, Universidade Federal de Alagoas

Analysis of PDEs Differential Geometry mathscidoc:1701.03016

Arkiv for Matematik, 1-9, 2015.9
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.
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@inproceedings{hilário2015stable,
  title={Stable hypersurfaces with zero scalar curvature in Euclidean space},
  author={Hilário Alencar, Manfredo do Carmo, and Gregório Silva Neto},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203407426235821},
  booktitle={Arkiv for Matematik},
  pages={1-9},
  year={2015},
}
Hilário Alencar, Manfredo do Carmo, and Gregório Silva Neto. Stable hypersurfaces with zero scalar curvature in Euclidean space. 2015. In Arkiv for Matematik. pp.1-9. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203407426235821.
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