David Tewodrose: Critical metrics of eigenvalue functionals via subdifferential

(13 mai 2024/May 13, 2024) Seminar Spectral Geometry in the clouds
https://agirouard.mat.ulaval.ca/Spect...

David Tewodrose (Vrije Universiteit Brussel): Critical metrics of eigenvalue functionals via subdifferential

Abstract: I will present a joint work with Romain Petrides (Universit´e Paris Cit´e) where we propose a general approach to study mapping properties of critical points of functionals F(g) = F(Sg), where g runs over an open set of Riemannian metrics on a given smooth manifold, Sg is a set of eigenvalues depending on g and F is a locally Lipschitz function. At the core of our approach is Clarke’s notion of subdifferential. Our work covers well-known cases, like Laplace and Steklov eigenvalues, and provides promising perspectives on new situations.