I will describe a joint program with Nikolai Nadirashvili dealing with upper bounds on eigenvalues of the Laplace-Beltrami operator on Riemannian surfaces in conformal classes. We prove the existence of extremal metrics and as an application, we obtain a new isoperimetric bound on the third eigenvalue on the 2-sphere.
Geometry-Topology Seminar
Thursday, March 3, 2016 - 5:45pm
Yannick Sire
Univ. Aix-Marseille and Johns Hopkins Univ.