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An isoperimetric problem for leaky loops and related mean-chord inequalities

Pavel Exner

TBD mathscidoc:1910.43062

Journal of mathematical physics, 46, (6), 062105, 2005.6
We consider a class of Hamiltonians in L2(R2) with attractive interaction supported by piecewise C2 smooth loops of a fixed length L, formally given by (x) with >0. It is shown that the ground state of this operator is locally maximized by a circular . We also conjecture that this property holds globally and show that the problem is related to an interesting family of geometric inequalities concerning mean values of chords of .
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@inproceedings{pavel2005an,
  title={An isoperimetric problem for leaky loops and related mean-chord inequalities},
  author={Pavel Exner},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020123652697175591},
  booktitle={Journal of mathematical physics},
  volume={46},
  number={6},
  pages={062105},
  year={2005},
}
Pavel Exner. An isoperimetric problem for leaky loops and related mean-chord inequalities. 2005. Vol. 46. In Journal of mathematical physics. pp.062105. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020123652697175591.
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