UBC DG-MP-PDE Seminar: Alexandre Girouard

We obtain upper bounds for the Steklov eigenvalues of warped products Ω×hΣ, where Ω is a compact Riemannian manifold with boundary and Σ is a closed Riemannian manifold, under assumptions on the Lp-norm of the warping function h. The upper bounds that we obtain are very different depending on the dimension n of the fiber Σ and the value of p. In some cases, we obtain optimal upper bounds and stability estimates. This is joint work with Jade Brisson, Bruno Colbois and Katie Gittins.