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.
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The authors would like to thank the referee for his/her valuable suggestions and useful comments which improved the paper.
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The second and fourth authors are partially supported by CNPq, Brazil, grants 303977/2015-9 and 308757/2015-7.
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de Lima, E.L., de Lima, H.F., dos Santos, F.R. et al. Sharp eigenvalue estimates of closed H-hypersurfaces in locally symmetric spaces. Czech Math J 69, 969–981 (2019). https://doi.org/10.21136/CMJ.2019.0562-17
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DOI: https://doi.org/10.21136/CMJ.2019.0562-17