Bounding the eigenvalues of the Laplace-Beltrami operator on compact submanifolds

Bruno Colbois, Emily B. Dryden, Ahmad El Soufi

We give upper bounds for the eigenvalues of the La-place-Beltrami operator of a compact $m$-dimensional submanifold $M$ of ${\mathbb{R}}^{m+p}$. Besides the dimension and the volume of the s…