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New estimates for the first eigenvalue of the Jacobi operator on closed hypersurfaces in Riemannian space forms. (English) Zbl 07250695

Summary: We study the first eigenvalue of the Jacobi operator on closed hypersurfaces with constant mean curvature in non-flat Riemannian space forms. Under an appropriate constraint on the totally umbilical tensor of the hypersurfaces and following J. Meléndez’s ideas in [Bull. Braz. Math. Soc. (N.S.) 45, No. 3, 385–404 (2014; Zbl 1319.53065)] we obtain a new sharp upper bound of the first eigenvalue of the Jacobi operator.

MSC:

58J50 Spectral problems; spectral geometry; scattering theory on manifolds

Citations:

Zbl 1319.53065
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References:

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