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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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
Key words and phrases
- weighted conformally stationary spacetime
- weighted GRW spacetime
- closed spacelike hypersurface
- f-stability
- strong f-stability