Czechoslovak Mathematical Journal, first online, pp. 1-13
Sharp eigenvalue estimates of closed $H$-hypersurfaces in locally symmetric spaces
Eudes L. de Lima, Henrique F. de Lima, Fábio R. dos Santos, Marco A. L. Velásquez
Received December 10, 2017. Published online March 28, 2019.
Abstract: 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.