Geometrically induced discrete spectrum in curved tubes

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

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Spectral Theory, Mathematical Physics, Differential Geometry, 81Q10, 58J50, 53A04

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http://salesiana.dossiersoluciones.com/handle/123456789/95033

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0412132
 http://arxiv.org/abs/math/0412132
 Differential Geom. Appl. 23 (2005), no. 2, 95-105.

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arXiv