Title: “ Isoperimetry and extremal metrics on Riemannian manifolds”
Speaker: Yannik Sire
Speaker Info: Johns Hopkins Univ.
I will report on a joint program initiated with N. Nadirashvili about the existence and regularity of critical metrics (in conformal classes) of eigenvalues of the Laplace-Beltrami operator. There are deep links between such metrics and minimal surfaces in euclidean spheres. I will explain how to build such metrics and provide several applications on isoperimetry on the 2-sphere and the real projective plane. Then I will move on to the higher dimensional case where the situation is trickier and only partial results are available. I will describe several on-going projects and open problems.Date: Monday, January 14, 2019