Critical Metrics of Eigenvalue Functionals via Subdifferential

Explore a comprehensive seminar on spectral geometry focusing on critical metrics of eigenvalue functionals through subdifferential analysis. Delve into David Tewodrose's joint work with Romain Petrides, which proposes a general approach to studying mapping properties of critical points for functionals F(g) = F(Sg). Examine how this method applies to Riemannian metrics on smooth manifolds, where Sg represents a set of eigenvalues dependent on g, and F is a locally Lipschitz function. Discover the central role of Clarke's subdifferential concept in this approach. Learn how this work encompasses well-known cases such as Laplace and Steklov eigenvalues while offering promising perspectives on new situations in the field of spectral geometry.