In this talk we explore the interplay between the eigenvalues of the Steklov problem and the geometry of the underlying manifold via geometric upper bounds for the Steklov eigenvalues.
We present isoperimetric-type upper bounds for the Steklov eigenvalues of warped product manifolds. In addition, we investigate the maximisation of the Steklov eigenvalues when the warping functions are subject to certain geometric constraints.
Time-permitting, we present results regarding upper bounds for the Steklov eigenvalues, ratios, and gaps in the particular case of balls with revolution-type metrics.
This is based on joint work with Jade Brisson, Bruno Colbois, and Alexandre Girouard.
