| Résume | We study the spectral gap for the Steklov problem on a Riemannian manifold. When a manifold has only one boundary component, it is known that the geometry of a boundary collar alone can provide a lower bound on the spectral gap. We therefore focus on manifolds with at least two boundary components. We show how the interior geometry can influence the spectral gap and establish a new connection between Steklov spectral gaps and the Neumann eigenvalues of interior subdomains. We then discuss applications of this connection to negatively curved manifolds. It is based on joint work with Tirumala Chakradhar and Bruno Colbois. |
