Alexandre Girouard

Isoperimetric-type upper bounds for Steklov eigenvalues of warped products

We obtain isoperimetric-type upper bounds for the Steklov eigenvalues of Riemannian warped products D x_h Σ, where D is compact with boundary and Σ is closed. The bounds depend on volume, dimension and L^p norms of the warping function h. The bounds are sharp and in some cases we obtain quantitative stability improvement. This is based on joint work with Jade Brisson, Bruno Colbois and Katie Gittins.