Title: High-frequency approximation of the interior dirichlet-to-neumann map and applications to the transmission eigenvalues,
Abstract: We study the high-frequency behavior of the Dirichlet-to-Neumann map for an
arbitrary compact Riemannian manifold with a non-empty smooth boundary. We show
that far from the real axis it can be approximated by a simpler operator. We
use this fact to get new results concerning the location of the transmission
eigenvalues on the complex plane. In some cases we obtain optimal transmission
eigenvalue-free regions.