Geometrically induced discrete spectrum in curved tubes

Details Geometrically induced discrete spectrum in curved tubes Geometrically induced discrete spectrum in curved tubes

2004-12-07

arxiv.org/abs/math/0412132v1

Differential Geom. Appl. 23 (2005), no. 2, 95-105.

Mathematics

Spectral Theory

LaTeX, 13 pages; to appear in Differential Geometry and its Applications

Scientific paper

The Dirichlet Laplacian in curved tubes of arbitrary cross-section rotating with respect to 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.

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