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A lower bound to the spectral threshold in curved tubes

Pavel Exner P Freitas D Krejik

TBD mathscidoc:1910.43061

Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 460, (2052), 3457-3467, 2004.12
We consider the Laplacian in curved tubes of arbitrary crosssection 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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@inproceedings{pavel2004a,
  title={A lower bound to the spectral threshold in curved tubes},
  author={Pavel Exner, P Freitas, and D Krejik},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020123614091280590},
  booktitle={Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences},
  volume={460},
  number={2052},
  pages={3457-3467},
  year={2004},
}
Pavel Exner, P Freitas, and D Krejik. A lower bound to the spectral threshold in curved tubes. 2004. Vol. 460. In Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences. pp.3457-3467. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020123614091280590.
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