| Title:
|
A new characterization of $r$-stable hypersurfaces in space forms (English) |
| Author:
|
de Lima, H. F. |
| Author:
|
Velásquez, M. A. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
47 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
119-131 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we study the $r$-stability of closed hypersurfaces with constant $r$-th mean curvature in Riemannian manifolds of constant sectional curvature. In this setting, we obtain a characterization of the $r$-stable ones through of the analysis of the first eigenvalue of an operator naturally attached to the $r$-th mean curvature. (English) |
| Keyword:
|
space forms |
| Keyword:
|
$r$-th mean curvatures |
| Keyword:
|
$r$-stability |
| MSC:
|
53B30 |
| MSC:
|
53C42 |
| MSC:
|
53C50 |
| MSC:
|
53Z05 |
| MSC:
|
83C99 |
| idZBL:
|
Zbl 1249.53081 |
| idMR:
|
MR2813538 |
| . |
| Date available:
|
2011-06-06T14:42:04Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141561 |
| . |
| Reference:
|
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| Reference:
|
[2] Barbosa, J. L. M., Colares, A. G.: Stability of hypersurfaces with constant $r$-mean curvature.Ann. Global Anal. Geom. 15 (1997), 277–297. Zbl 0891.53044, MR 1456513, 10.1023/A:1006514303828 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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[8] de Lima, H. F.: Spacelike hypersurfaces with constant higher order mean curvature in de Sitter space.J. Geom. Phys. 57 (2007), 967–975. Zbl 1111.53049, MR 2275203, 10.1016/j.geomphys.2006.07.005 |
| Reference:
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[9] He, Y., Li, H.: Stability of area-preserving variations in space forms.Ann. Global Anal. Geom. 34 (2008), 55–68. Zbl 1156.53037, MR 2415178, 10.1007/s10455-007-9095-3 |
| Reference:
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| Reference:
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| Reference:
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| . |
