Geodesic
Sharp eigenvalue estimates of closed $H$-hypersurfaces in locally symmetric spaces
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 4, pp. 969-981
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The purpose of this article is to obtain sharp estimates for the first eigenvalue of the stability operator of constant mean curvature closed hypersurfaces immersed into locally symmetric Riemannian spaces satisfying suitable curvature conditions (which includes, in particular, a Riemannian space with constant sectional curvature). As an application, we derive a nonexistence result concerning strongly stable hypersurfaces in these ambient spaces.
The purpose of this article is to obtain sharp estimates for the first eigenvalue of the stability operator of constant mean curvature closed hypersurfaces immersed into locally symmetric Riemannian spaces satisfying suitable curvature conditions (which includes, in particular, a Riemannian space with constant sectional curvature). As an application, we derive a nonexistence result concerning strongly stable hypersurfaces in these ambient spaces.
DOI : 10.21136/CMJ.2019.0562-17
Classification : 53A10, 53C42
Keywords: locally symmetric Riemannian space; closed $H$-hypersurface; strong stability; first stability eigenvalue 
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     author = {de Lima, Eudes L. and de Lima, Henrique F. and dos Santos, F\'abio R. and Vel\'asquez, Marco A. L.},
     title = {Sharp eigenvalue estimates of closed $H$-hypersurfaces in locally symmetric spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {969--981},
     year = {2019},
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     number = {4},
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     mrnumber = {4039613},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2019.0562-17/}
}
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de Lima, Eudes L.; de Lima, Henrique F.; dos Santos, Fábio R.; Velásquez, Marco A. L. Sharp eigenvalue estimates of closed $H$-hypersurfaces in locally symmetric spaces. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 4, pp. 969-981. doi: 10.21136/CMJ.2019.0562-17

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