Zoom link: https://princeton.zoom.us/j/594605776

I will report on joint work with Matthew J. Gursky in which we consider the problem of extremizing eigenvalues of the Conformal Laplacian in fixed conformal classes. I will explain the connection of these extremal metrics to constant curvature metrics (Yamabe metrics), to the existence of harmonic maps into spheres, and to the existence of nodal solutions to a Yamabe type equation (first noticed by Ammann-Humbert). If time permits, I will also explain the analogous problem for the eigenvalues of the Conformal Dirichlet-to-Robin map on manifolds with boundary.