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Keywords:
locally symmetric Riemannian space; closed $H$-hypersurface; strong stability; first stability eigenvalue
locally symmetric Riemannian space; closed $H$-hypersurface; strong stability; first stability eigenvalue
Summary:
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.
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