Stable space-like hypersurfaces in the de Sitter space
Liu, Ximin ; Junlei, Deng
Archivum Mathematicum, Tome 040 (2004), p. 111-117 / Harvested from Czech Digital Mathematics Library
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In this paper, we study the stability of space-like hypersurfaces with constant scalar curvature immersed in the de Sitter spaces.

Publié le : 2004-01-01
Classification:  53B25,  53B30,  53C42,  53C50 
@article{107895,
     author = {Ximin Liu and Deng Junlei},
     title = {Stable space-like hypersurfaces in the de Sitter space},
     journal = {Archivum Mathematicum},
     volume = {040},
     year = {2004},
     pages = {111-117},
     zbl = {1114.53057},
     mrnumber = {2068685},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107895}
}

Liu, Ximin; Junlei, Deng. Stable space-like hypersurfaces in the de Sitter space. Archivum Mathematicum, Tome 040 (2004) pp. 111-117. http://gdmltest.u-ga.fr/item/107895/

Alencar H.; Do Carmo M.; Colares A. G. Stable hypersurfaces with constant scalar curvature, Math. Z. 213 (1993), 117–131. (1993) | MR 1217674 | Zbl 0792.53057

Akutagawa K. On space-like hypersurfaces with constant mean curvature in the de Sitter space, Math. Z. 196 (1987), 13–19. (196 ) | MR 0907404

Barbosa J. L.; Do Carmo M. Stability of hypersurfaces with constant mean curvature, Math. Z. 185 (1984), 339–353. (1984) | MR 0731682 | Zbl 0513.53002

Barbosa J. L.; Do Carmo M.; Eschenburg J. Stability of hypersurfaces of constant mean curvature in Riemannian manifolds, Math. Z. 197 (1988), 123–138. (197 ) | MR 0917854

Barbosa J. L.; Oliker V. Stable spacelike hypersurfaces with constant mean curvature in Lorentz space, Geometry and Global Analysis, Tohoku University, Sendai (1993), 161–164. (1993) | MR 1361178 | Zbl 0974.53513

Cheng Q. M. Complete space-like submanifolds in a de Sitter space with parallel mean curvature vector, Math. Z. 206 (1991), 333–339. (1991) | MR 1095758 | Zbl 0695.53042

Cheng S. Y.; Yau S. T. Hypersurfaces with constant scalar curvature, Math. Ann. 225 (1977), 195–204. (1977) | MR 0431043 | Zbl 0349.53041

Ramanathan J. Complete space-like hypersurfaces of constant mean curvature in the de Sitter space, Indiana Univ. Math. J. 36 (1987), 349–359. (1987) | MR 0891779

Reilly R. C. Variational properties of functions of the mean curvatures for hypersurfaces in space forms, J. Differential Geom. 8 (1973), 465–477. (1973) | MR 0341351 | Zbl 0277.53030