EVENT DETAILS AND ABSTRACT

Title: How large can a Steklov eigenvalue be?
Speaker: Alexandre Girouard
Speaker Info: U Laval
Brief Description:
Special Note:
Abstract:

The Dirichlet-to-Neumann operator D is a naturally occurring elliptic operator acting on smooth functions f:M--->R defined on the boundary M of a compact Riemannian manifold X. Its eigenvalues are known as the Steklov eigenvalues of X. The general topic of my talk will be isoperimetric bounds for Steklov eigenvalues. The focus will be on upper bounds for star-shaped and simply connected Euclidean domains (joint with R. Laugesen and B. Siudeja) and for compact surfaces (joint with I. Polterovich). I will also discuss a discretization procedure leading to the construction of compact surfaces with boundary of fixed length and with arbitrarily large spectral gap (joint with B. Colbois) as well as conformal deformations on compact Riemannian manifolds.