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Spectral estimates for Dirichlet Laplacians and Schrdinger operators on geometrically nontrivial cusps

Pavel Exner Diana Barseghyan

TBD mathscidoc:1910.43231

arXiv preprint arXiv:1203.2098, 2012.3
The goal of this paper is to derive estimates of eigenvalue moments for Dirichlet Laplacians and Schrdinger operators in regions having infinite cusps which are geometrically nontrivial being either curved or twisted; we are going to show how those geometric properties enter the eigenvalue bounds. The obtained inequalities reflect the essentially one-dimensional character of the cusps and we give an example showing that in an intermediate energy region they can be much stronger than the usual semiclassical bounds.
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@inproceedings{pavel2012spectral,
  title={Spectral estimates for Dirichlet Laplacians and Schrdinger operators on geometrically nontrivial cusps},
  author={Pavel Exner, and Diana Barseghyan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020134041455711760},
  booktitle={arXiv preprint arXiv:1203.2098},
  year={2012},
}
Pavel Exner, and Diana Barseghyan. Spectral estimates for Dirichlet Laplacians and Schrdinger operators on geometrically nontrivial cusps. 2012. In arXiv preprint arXiv:1203.2098. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020134041455711760.
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