A lower bound to the spectral threshold in curved tubes

Details A lower bound to the spectral threshold in curved tubes A lower bound to the spectral threshold in curved tubes

2004-05-13

arxiv.org/abs/math-ph/0405039v1

R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 460 (2004), no. 2052, 3457-3467

Physics

Mathematical Physics

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

Scientific paper

10.1098/rspa.2004.1356

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.

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