Spectrum of Dirichlet Laplacian in a conical layer

Abstract

Abstract. We study 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 one there is an infinite sequence of isolated eigenvalues and analyze properties of these geometrically induced bound states. By numerical computation we find examples of the eigenfunctions. Spectrum of Dirichlet Laplacian in a conical layer 2 1.