Séminaire de GéométrieGeneral approach to Buser's type upper bounds for eigenvalues
jeudi 15 mars 2012 14:00 - Tours - Salle 2290 (Bât E2)
There are deep connections between eigenvalues of "natural operators" on manifolds and their geometric data. One of the most considered geometric invariant is the Ricci curvature. In 1980, Buser obtained an upper bound for the k'th eigenvalues of the Laplace-Beltrami operator on Riemannian manifolds in terms of the lower bound of the Ricci curvature, the volume of the manifold and k. We investigate Buser's type inequality in an abstract fashion so that it works in a great generality. We illustrate the result in two interesting examples.