| Title:
|
Stable space-like hypersurfaces in the de Sitter space (English) |
| Author:
|
Liu, Ximin |
| Author:
|
Junlei, Deng |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
40 |
| Issue:
|
2 |
| Year:
|
2004 |
| Pages:
|
111-117 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we study the stability of space-like hypersurfaces with constant scalar curvature immersed in the de Sitter spaces. (English) |
| Keyword:
|
space-like hypersurface |
| Keyword:
|
stablity |
| Keyword:
|
scalar curvature |
| Keyword:
|
de Sitter space |
| MSC:
|
53B25 |
| MSC:
|
53B30 |
| MSC:
|
53C42 |
| MSC:
|
53C50 |
| idZBL:
|
Zbl 1114.53057 |
| idMR:
|
MR2068685 |
| . |
| Date available:
|
2008-06-06T22:43:05Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107895 |
| . |
| Reference:
|
[1] Alencar H., do Carmo M., Colares A. G.: Stable hypersurfaces with constant scalar curvature.Math. Z. 213 (1993), 117–131. Zbl 0792.53057, MR 1217674 |
| Reference:
|
[2] Akutagawa K.: On space-like hypersurfaces with constant mean curvature in the de Sitter space.Math. Z. 196 (1987), 13–19. MR 0907404 |
| Reference:
|
[3] Barbosa J. L., do Carmo M.: Stability of hypersurfaces with constant mean curvature.Math. Z. 185 (1984), 339–353. Zbl 0513.53002, MR 0731682 |
| Reference:
|
[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. MR 0917854 |
| Reference:
|
[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. Zbl 0974.53513, MR 1361178 |
| Reference:
|
[6] Cheng Q. M.: Complete space-like submanifolds in a de Sitter space with parallel mean curvature vector.Math. Z. 206 (1991), 333–339. Zbl 0695.53042, MR 1095758 |
| Reference:
|
[7] Cheng S. Y., Yau S. T.: Hypersurfaces with constant scalar curvature.Math. Ann. 225 (1977), 195–204. Zbl 0349.53041, MR 0431043 |
| Reference:
|
[8] Ramanathan J.: Complete space-like hypersurfaces of constant mean curvature in the de Sitter space.Indiana Univ. Math. J. 36 (1987), 349–359. MR 0891779 |
| Reference:
|
[9] Reilly R. C.: Variational properties of functions of the mean curvatures for hypersurfaces in space forms.J. Differential Geom. 8 (1973), 465–477. Zbl 0277.53030, MR 0341351 |
| . |
