Spectral analysis in broken sheared waveguides

Abstract

Let be a broken sheared waveguide; that is, is built by translating a cross‐section (an arbitrary bounded connected open set of ) in a constant direction along a broken line in . We prove that the discrete spectrum of the Dirichlet Laplacian operator in is non‐empty and finite. Furthermore, we show a particular geometry for , which implies that the total multiplicity of the discrete spectrum is equal to 1.