« Fundamental gap » et liens entre les valeurs propres du Laplacien Dirichlet et Neumann et la géométrie de Bakry-Émery.

For a convex domain in \R^n, the so-called ``fundamental gap'' is the difference between the first two Dirichlet eigenvalues of the (Euclidean) Laplacian. In this talk, I will discuss joint work with Z. Lu concerning the fundamental gap on simplicial domains in \R^n, connections between the gap and Bakry-Émery geometry, and a recent result relating the Dirichlet problem in \R^n to a certain the Neumann problem in \R^{n+1}.