Geodesic
A new characterization of $r$-stable hypersurfaces in space forms
Archivum mathematicum, Tome 47 (2011) no. 2, pp. 119-131.

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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.
Classification : 53B30, 53C42, 53C50, 53Z05, 83C99
Keywords: space forms; $r$-th mean curvatures; $r$-stability 
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     title = {A new characterization of $r$-stable hypersurfaces in space forms},
     journal = {Archivum mathematicum},
     pages = {119--131},
     publisher = {mathdoc},
     volume = {47},
     number = {2},
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     zbl = {1249.53081},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2011__47_2_a5/}
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de Lima, H. F.; Velásquez, M. A. A new characterization of $r$-stable hypersurfaces in space forms. Archivum mathematicum, Tome 47 (2011) no. 2, pp. 119-131. http://geodesic.mathdoc.fr/item/ARM_2011__47_2_a5/