The bounds for the squared norm of the second fundamental form of minimal submanifolds of .
New estimates for the first eigenvalue of the Jacobi operator on closed hypersurfaces in Riemannian space forms
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 Meléndez's ideas in J. Meléndez (2014) we obtain a new sharp upper bound of the first eigenvalue of the Jacobi operator.
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