Stable hypersurfaces with zero scalar curvature in Euclidean space

Stable hypersurfaces with zero scalar curvature in Euclidean space

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-Kr...

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Veröffentlicht in:Arkiv för matematik 2016-10, Vol.54 (2), p.233-241
Hauptverfasser: Alencar, Hilário, do Carmo, Manfredo, Neto, Gregório Silva
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Curvature
Dimensional stability
Euclidean geometry
Euclidean space
Geometry
Mathematics
Mathematics and Statistics
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description 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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source International Press Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Project Euclid Open Access; SpringerLink Journals - AutoHoldings
subjects Curvature
Dimensional stability
Euclidean geometry
Euclidean space
Geometry
Mathematics
Mathematics and Statistics
title Stable hypersurfaces with zero scalar curvature in Euclidean space
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