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Strong (r, s)-stability in the de Sitter space

Published online by Cambridge University Press:  30 January 2015

Henrique F. de Lima ,
Antonio F. de Sousa  and
Marco Antonio L. Velásquez
Henrique F. de Lima
Affiliation:
Departamento de Matemática, Universidade Federal de Campina Grande, 58109-970 Campina Grande, Paraíba, Brazil, ([email protected])
Antonio F. de Sousa
Affiliation:
Departamento de Matemática, Universidade Federal de Pernambuco, 50740-560 Recife, Pernambuco, Brazil
Marco Antonio L. Velásquez
Affiliation:
Departamento de Matemática, Universidade Federal de Campina Grande, 58109-970 Campina Grande, Paraíba, Brazil
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Abstract

In this paper, we establish the notion of strong (r, s)-stability concerning closed space-like hypersurfaces immersed with higher-order mean curvatures linearly related in the de Sitter space . In this setting, we prove that totally umbilical round spheres of are strongly (r, s)-stable. Afterwards, we obtain sufficient geometric conditions that guarantee that a closed strongly (r, s)-stable space-like hypersurface in must be a totally umbilical round sphere.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 1 , February 2015 , pp. 91 - 104
Copyright
Copyright © Royal Society of Edinburgh 2015 

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