f-stability of spacelike hypersurfaces in weighted spacetimes

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...

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Bibliographic Details
Published in:Acta mathematica Hungarica 2017-12, Vol.153 (2), p.334-349
Main Authors: de Lima, H. F., Oliveira, A. M. S., Santos, M. S., Velásquez, M. A. L.
Format: Article
Language:English
Subjects:
Curvature
Geometry
Mathematical analysis
Mathematics
Mathematics and Statistics
Stability
Weighting functions
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Summary: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 .
ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-017-0731-5