SFU MOCAD Seminar: Alexandre Girouard

We investigate the Steklov eigenvalue problem in the exterior of a bounded Euclidean domain. In particular, we prove the equivalence of several formulations of this problem previously proposed in the literature. We derive geometric eigenvalue inequalities and examine other properties of the exterior Steklov eigenvalues and eigenfunctions. Our results reveal that while there are many similarities between the exterior and the interior Steklov problems, certain spectral phenomena differ significantly. We also emphasise the distinctions between the properties of the exterior Steklov problem in two dimensions and in higher dimensions. Joint work with Lukas Bundrock, Denis Grebenkov, Michael Levitin and Iosif Polterovich.