Abstract
We obtain upper bounds for the first eigenvalue of the linearized operator $L_r$ of the $r$-mean curvature of a compact manifold immersed in a space of constant curvature $\delta$. By the same method, we obtain an upper bound for the first eigenvalue of the stability operator associated to $L_r$ when $\delta < 0$.
Citation
Hilário Alencar. Fernando Marques. Manfredo do Carmo. "Upper bounds for the first eigenvalue of the operator $L\sb r$ and some applications." Illinois J. Math. 45 (3) 851 - 863, Fall 2001. https://doi.org/10.1215/ijm/1258138155
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