Antoine Métras

Steklov eigenvalues optimisation on manifolds

In this talk, I will discuss the optimisation problem of Steklov eigenvalues under variation of the metric on a manifold. I will summarize some known results on surface, in particular the relationship between critical metric, their associated eigenfunctions, and free-boundary harmonic maps to balls. I will then explain how those results can be generalised to higher dimensions and how the problem needs to be modified to allow for this generalisation. This is a joint work with Mikhail Karpukhin.