David Tewodrose

Critical points of eigenvalue functionals

I will present a work in progress with Romain Petrides (Université Paris Cité) where we develop an abstract framework to tackle spectral optimization problems. Based on Clarke’s non-smooth analysis, our approach yields an Euler-Lagrange characterization of critical points of functions of the form $F(\lambda_1,\ldots,\lambda_N)$ where F is C1 and the $\lambda_i$ are eigenvalues. I will describe our setting and illustrate it with some examples including the case of critical metrics for the Laplace eigenvalues in a given conformal class over a smooth compact surface with empty boundary.