Geometrically induced discrete spectrum in curved tubes
Spectral Theory
2007-05-23 v1 Mathematical Physics
Differential Geometry
math.MP
Abstract
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.
Cite
@article{arxiv.math/0412132,
title = {Geometrically induced discrete spectrum in curved tubes},
author = {B. Chenaud and P. Duclos and P. Freitas and D. Krejcirik},
journal= {arXiv preprint arXiv:math/0412132},
year = {2007}
}
Comments
LaTeX, 13 pages; to appear in Differential Geometry and its Applications