Geometrically induced discrete spectrum in curved tubes. (English) Zbl 1078.81022

Summary: The Dirichlet Laplacian in curved tubes of arbitrary cross-section rotating w.r.t. the Tang frame along infinite curves in Euclidean spaces of arbitrary dimension is investigated. If the reference curve is not straight and its curvatures vanish at infinity, we prove that the essential spectrum as a set coincides with the spectrum of the straight tube of the same cross-section and that the discrete spectrum is not empty.


81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35P05 General topics in linear spectral theory for PDEs
47F05 General theory of partial differential operators
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