### Steklov eigenvalues optimisation on manifolds

Analysis and Geometry Seminar

10th November 2022, 3:15 pm – 4:15 pm

Fry Building, 2.04

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.

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