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f-stability of spacelike hypersurfaces in weighted spacetimes

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Abstract

We establish the notions of f-stability and strong f-stability concerning closed spacelike hypersurfaces immersed with constant f-mean curvature in a conformally stationary spacetime endowed with a conformal timelike vector field V and a weight function f. When V is closed, with the aid of the f-Laplacian of a suitable support function, we characterize f-stable closed spacelike hypersurfaces through the analysis of the first eigenvalue of the Jacobi operator associated to the corresponding variational problem. Furthermore, we obtain sufficient conditions which assure that a strongly f-stable closed spacelike hypersurface must be either f-maximal or isometric to a leaf orthogonal to V.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Campina Grande, 58429-970, Campina Grande, Paraíba, Brazil

    H. F. de Lima, A. M. S. Oliveira & M. A. L. Velásquez

  2. Departamento de Matemática, Universidade Federal da Paraíba, 58.051-900, João Pessoa, Paraíba, Brazil

    M. S. Santos

Authors
  1. H. F. de Lima
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  2. A. M. S. Oliveira
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  3. M. S. Santos
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  4. M. A. L. Velásquez
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Corresponding author

Correspondence to H. F. de Lima.

Additional information

The first author is partially supported by CNPq, Brazil, grant 303977/2015-9.

The second author is partially supported by CAPES, Brazil.

The fourth author is partially supported by CNPq, Brazil, grant 308757/2015-7.

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de Lima, H.F., Oliveira, A.M.S., Santos, M.S. et al. f-stability of spacelike hypersurfaces in weighted spacetimes. Acta Math. Hungar. 153, 334–349 (2017). https://doi.org/10.1007/s10474-017-0731-5

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  • DOI: https://doi.org/10.1007/s10474-017-0731-5

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