Bounds on the eigenvalues of Laplace-Beltrami operators and Witten Laplacians on Riemannian manifolds

Math Physics Seminar
Friday, April 19, 2013 - 3:00pm
1 hour (actually 50 minutes)
Skiles 006
Université François Rabelais, Tours, France

El Soufi will be visiting Harrell for the week leading up to this seminar

We shall survey some of the classical and recent results giving upper bounds of the eigenvalues of the Laplace-Beltrami operator on a compact Riemannian manifold (Yang-Yau, Korevaar, Grigor'yan-Netrusov-Yau, etc.).  Then we discuss extensions of these results to the eigenvalues  of Witten Laplacians associated to weighted volume measures and investigate bounds of these eigenvalues in terms of suitable norms of the weights.