Geometrically induced discrete spectrum in curved tubes

B. Chenaud; D. Krejcirik; P. Duclos; P. Freitas

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Geometrically induced discrete spectrum in curved tubes

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arxiv math/0412132 v1 pith:6Q7YDJDY submitted 2004-12-07 math.SP math-phmath.DGmath.MP

Geometrically induced discrete spectrum in curved tubes

B. Chenaud , P. Duclos , P. Freitas , D. Krejcirik This is my paper

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keywords spectrumarbitrarycross-sectioncurveddiscretestraighttubesalong

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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.

Geometrically induced discrete spectrum in curved tubes

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