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Stable compact spacelike hypersurfaces in the de Sitter space as maxima of a linear combination of area and volume

  • Marco A. L. Velásquez
  • Henrique F. de Lima
  • Jonatan F. da Silva
  • Arlandson M. S. Oliveira
Article
  • 21 Downloads

Abstract

We define the notion of strong (rsab)-stability concerning compact space-like hypersurfaces immersed in the de Sitter space \(\mathbb {S}^{n+1}_1\). We study the variational problem of maximizing a certain Jacobi functional given by a linear combination of area and volume. Under a suitable constraint on a constant that appears in the computation of the second variation of this functional, we prove that a compact space-like hypersurface \(M^n\) contained in a a chronological future (or past) of \(\mathbb {S}^{n+1}_1\), with positive \((s+1)\)th curvature and such that \(H\le 1\), must be a totally umbilical round sphere.

Mathematics Subject Classification

Primary 53C42 Secondary 53B30 53C40 53C50 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade Federal de Campina GrandeCampina GrandeBrazil
  2. 2.Departamento de MatemáticaUniversidade Federal do CearáFortalezaBrazil

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