Spectral continuity — criteria and applications
In this talk, I will discuss some synthetic and easy to verify criteria for eigenvalues and eigenfunctions of Laplace-type operators to vary continuously with respect to some parametric families. The Laplace and Steklov problem will give us meaningful illustrative examples, and I will also discuss applications outside of spectral theory. In particular, this framework allows one to find a relationship between free boundary minimal surfaces in the ball and minimal surfaces in the sphere. This is based on joint work with A. Girouard and M. Karpukhin.