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.
Keywords:  locally symmetric Riemannian space; closed $H$-hypersurface; strong stability; first stability eigenvalue
Classification MSC:  53C42, 53A10
DOI:  10.21136/CMJ.2019.0562-17

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Affiliations:   Eudes L. de Lima, Unidade Acadêmica de Ciências Exatas e da Natureza, Universidade Federal de Campina Grande, 58.900-000 Cajazeiras, Paraíba, Brazil, e-mail:; Henrique F. de Lima (corresponding author), Fábio R. dos Santos, Marco A. L. Velásquez, Departamento de Matemática, Universidade Federal de Campina Grande, 58.429-970 Campina Grande, Paraíba, Brazil, e-mail:,,

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