Spectrum of Dirichlet Laplacian in a conical layer

We study the spectral properties of Dirichlet Laplacian on the conical layer of the opening angle π − 2θ and thickness equal to π. We demonstrate that below the continuum threshold, which is equal to 1, there is an infinite sequence of isolated eigenvalues and analyse properties of these geometrically induced bound states. By numerical computation we find examples of the eigenfunctions.