The Steklov Problem on Surfaces with Finitely Smooth Boundary


The Steklov eigenvalue problem has been one of the central topics in spectral geometry over the last decade. In particular, a lot of research has been focused on the asymptotic distribution of Steklov eigenvalues. In this talk, we investigate asymptotics for Steklov eigenvalues on surfaces with a boundary that is only smooth to finite order. In particular, we obtain remainder estimates in Weyl’s law with a rate of decay depending on the order of smoothness.