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Topologically nontrivial quantum layers

G Carron Pavel Exner D Krejik

TBD mathscidoc:1910.43038

Journal of Mathematical Physics, 45, (2), 774-784, 2004.2
Given a complete noncompact surface embedded in R3, we consider the Dirichlet Laplacian in the layer that is defined as a tubular neighborhood of constant width about . Using an intrinsic approach to the geometry of , we generalize the spectral results of the original paper by Duclos et al. [Commun. Math. Phys. 223, 13 (2001)] to the situation when does not possess poles. This enables us to consider topologically more complicated layers and state new spectral results. In particular, we are interested in layers built over surfaces with handles or several cylindrically symmetric ends. We also discuss more general regions obtained by compact deformations of certain .
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@inproceedings{g2004topologically,
  title={Topologically nontrivial quantum layers},
  author={G Carron, Pavel Exner, and D Krejik},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020122656969607567},
  booktitle={Journal of Mathematical Physics},
  volume={45},
  number={2},
  pages={774-784},
  year={2004},
}
G Carron, Pavel Exner, and D Krejik. Topologically nontrivial quantum layers. 2004. Vol. 45. In Journal of Mathematical Physics. pp.774-784. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020122656969607567.
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