Bounding the eigenvalues of the Laplace-Beltrami operator on compact submanifolds
Bounding the eigenvalues of the Laplace-Beltrami operator on compact submanifolds
We give upper bounds for the eigenvalues of the La-place-Beltrami operator of a compact $m$-dimensional submanifold $M$ of $\R^{m+p}$. Besides the dimension and the volume of the submanifold and the order of the eigenvalue, these bounds depend on either the maximal number of intersection points of $M$ with a $p$-plane …