Upper bounds for Steklov eigenvalues

(16 Nov. 2020/Nov. 16, 2020) Seminar Spectral Geometry / Séminaire Spectral Geometry

Katie Gittins (Durham University, UK)

Upper bounds for Steklov eigenvalues

Abstract:
The relationship between the Steklov eigenvalues of a Riemannian manifold andthe geometry of its boundary has received a great deal of attention in recent years.One way to gain insight into this relationship is to obtain bounds for the Stekloveigenvalues in terms of some of the geometric quantities of the manifold and itsboundary. We first recall some known geometric upper bounds for the Stekloveigenvalues of a Riemannian manifold. We then consider the Steklov eigenvaluesof a submanifold of Euclidean space and present some geometric upper boundsinvolving the intersection index of the manifold and that of its boundary.This is based on joint work with Bruno Colbois (Université de Neuchâtel).