A lower bound to the spectral threshold in curved tubes

Abstract

We consider the Laplacian in curved tubes of arbitrary cross-section rotating together with the Frenet frame along curves in Euclidean spaces of arbitrary dimension, subject to Dirichlet boundary conditions on the cylindrical surface and Neumann conditions at the ends of the tube. We prove that the spectral threshold of the Laplacian is estimated from below by the lowest eigenvalue of the Dirichlet Laplacian in a torus determined by the geometry of the tube.

LaTeX, 13 pages; to appear in R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci

References in corpus (2)

• On the spectrum of curved quantum waveguides
• Geometrically induced discrete spectrum in curved tubes

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• Trapped modes in finite quantum waveguides
• Spectral estimates for a class of Schrödinger operators with infinite phase space and potential unbounded from below
• Bose-Einstein Condensation in Geometrically Deformed Tubes
• Geometrically induced discrete spectrum in curved tubes
• The Cheeger constant of curved strips
• Sharp Poincaré inequalities in a class of non-convex sets
• Location of the nodal set for thin curved tubes