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The bounds for the squared norm of the second fundamental form of minimal submanifolds of $S^{n + p}$ .

Liu, Jiancheng; Zhang, Qiuyan — 2007

Balkan Journal of Geometry and its Applications (BJGA)

New estimates for the first eigenvalue of the Jacobi operator on closed hypersurfaces in Riemannian space forms

Jiancheng Liu; Rong Mi — 2020

Czechoslovak Mathematical Journal

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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The bounds for the squared norm of the second fundamental form of minimal submanifolds of S n + p .

New estimates for the first eigenvalue of the Jacobi operator on closed hypersurfaces in Riemannian space forms

The bounds for the squared norm of the second fundamental form of minimal submanifolds of $S^{n + p}$ .