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On geometric perturbations of critical Schrdinger operators with a surface interaction

Pavel Exner Martin Fraas

TBD mathscidoc:1910.43132

Journal of Mathematical Physics, 50, (11), 112101, 2009.11
We study singular Schrdinger operators with an attractive interaction supported by a closed smooth surface AR3 and analyze their behavior in the vicinity of the critical situation where such an operator has empty discrete spectrum and a threshold resonance. In particular, we show that if A is a sphere and the critical coupling is constant over it, any sufficiently small smooth area-preserving radial deformation gives rise to isolated eigenvalues. On the other hand, the discrete spectrum may be empty for general deformations. We also derive a related inequality for capacities associated with such surfaces.
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@inproceedings{pavel2009on,
  title={On geometric perturbations of critical Schrdinger operators with a surface interaction},
  author={Pavel Exner, and Martin Fraas},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020130927633284661},
  booktitle={Journal of Mathematical Physics},
  volume={50},
  number={11},
  pages={112101},
  year={2009},
}
Pavel Exner, and Martin Fraas. On geometric perturbations of critical Schrdinger operators with a surface interaction. 2009. Vol. 50. In Journal of Mathematical Physics. pp.112101. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020130927633284661.
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