Event
Alexandre Girouard, Université Laval
Monday, November 20, 2017 14:00to15:00
Room 5340, Pav. André-Aisenstadt, CA
Steklov eigenvalues of submanifolds with prescribed boundary in Euclidean space.
Let S be a fixed closed (n-1)-dimensional submanifold of Euclidean space R^{n+1}. I will discuss upper and lower bounds for the Steklov eigenvalues sigma_k(M), where M is any compact manifold with boundary S. An upper bound will be given, in term of the volume of M. This is based on methods from metric geometry. In the particular situation where S is the unit sphere S^{n-1} (lying in a coordinate hyperplane) and M is an hypersurface of revolution, I will prove that sigma_k(M)geq sigma_k(B^n) with equality if and only M is the n-dimensional ball B^n. This based on joint work with Bruno Colbois (Neuchâtel) and Katie Gittins (MPIM Bonn).