Bruno Colbois

Bounds for Steklov eigenvalues of warped products

I will give sharp upper bounds for the Steklov eigenvalues of warped product between an interval [0, L] and a compact Riemannian manifold of dimension 2. I will also consider the case of revolution metrics on the ball of dimension n. In this situation, I will give sharp upper bound for the ratio of two consecutive eigenvalues, in the sense of a Payne-Polya-Weinberger inequality, and, in dimension 3, for the gap between two consecutive eigenvalues. These results are obtained in collaboration with Jade Brisson and Katie Gittins.