Stable space-like hypersurfaces in the de Sitter space

Ximin Liu; Deng Junlei

Archivum Mathematicum (2004)

  • Volume: 040, Issue: 2, page 111-117
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Liu, Ximin, and Junlei, Deng. "Stable space-like hypersurfaces in the de Sitter space." Archivum Mathematicum 040.2 (2004): 111-117. <http://eudml.org/doc/249285>.

@article{Liu2004,
abstract = {In this paper, we study the stability of space-like hypersurfaces with constant scalar curvature immersed in the de Sitter spaces.},
author = {Liu, Ximin, Junlei, Deng},
journal = {Archivum Mathematicum},
keywords = {space-like hypersurface; stablity; scalar curvature; de Sitter space; stability; scalar curvature},
language = {eng},
number = {2},
pages = {111-117},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Stable space-like hypersurfaces in the de Sitter space},
url = {http://eudml.org/doc/249285},
volume = {040},
year = {2004},
}

TY - JOUR
AU - Liu, Ximin
AU - Junlei, Deng
TI - Stable space-like hypersurfaces in the de Sitter space
JO - Archivum Mathematicum
PY - 2004
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 040
IS - 2
SP - 111
EP - 117
AB - In this paper, we study the stability of space-like hypersurfaces with constant scalar curvature immersed in the de Sitter spaces.
LA - eng
KW - space-like hypersurface; stablity; scalar curvature; de Sitter space; stability; scalar curvature
UR - http://eudml.org/doc/249285
ER -

References

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  1. Alencar H., do Carmo M., Colares A. G., Stable hypersurfaces with constant scalar curvature, Math. Z. 213 (1993), 117–131. (1993) Zbl0792.53057MR1217674
  2. Akutagawa K., On space-like hypersurfaces with constant mean curvature in the de Sitter space, Math. Z. 196 (1987), 13–19. (196) MR0907404
  3. Barbosa J. L., do Carmo M., Stability of hypersurfaces with constant mean curvature, Math. Z. 185 (1984), 339–353. (1984) Zbl0513.53002MR0731682
  4. 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) MR0917854
  5. 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) Zbl0974.53513MR1361178
  6. Cheng Q. M., Complete space-like submanifolds in a de Sitter space with parallel mean curvature vector, Math. Z. 206 (1991), 333–339. (1991) Zbl0695.53042MR1095758
  7. Cheng S. Y., Yau S. T., Hypersurfaces with constant scalar curvature, Math. Ann. 225 (1977), 195–204. (1977) Zbl0349.53041MR0431043
  8. Ramanathan J., Complete space-like hypersurfaces of constant mean curvature in the de Sitter space, Indiana Univ. Math. J. 36 (1987), 349–359. (1987) MR0891779
  9. Reilly R. C., Variational properties of functions of the mean curvatures for hypersurfaces in space forms, J. Differential Geom. 8 (1973), 465–477. (1973) Zbl0277.53030MR0341351

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