| Résume | In this talk, we study the first eigenvalue of the Jacobi operator on an integral
n-varifold with constant mean curvature in space forms.
We find optimal upper bounds and prove rigidity results characterizing the case when
they are attained.
These give a new characterization for certain Clifford tori and catenoids.
The talk is based on joint works with H. T. Dung, J.C. Pyo, and Hung Tran.
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