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On the critical exponent in an isoperimetric inequality for chords

Pavel Exner Martin Fraas Evans M Harrell II

TBD mathscidoc:1910.43202

Physics Letters A, 368, 1-6, 2007.8
The problem of maximizing the L p norms of chords connecting points on a closed curve separated by arc length u arises in electrostatic and quantum-mechanical problems. It is known that among all closed curves of fixed length, the unique maximizing shape is the circle for 1 p 2, but this is not the case for sufficiently large values of p. Here we determine the critical value p c (u) of p above which the circle is not a local maximizer finding, in particular, that p c (1 2 L)= 5 2. This corrects a claim made in [P. Exner, EM Harrell, M. Loss, Lett. Math. Phys. 75 (2006) 225].
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@inproceedings{pavel2007on,
  title={On the critical exponent in an isoperimetric inequality for chords},
  author={Pavel Exner, Martin Fraas, and Evans M Harrell II},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020133149671879731},
  booktitle={Physics Letters A},
  volume={368},
  pages={1-6},
  year={2007},
}
Pavel Exner, Martin Fraas, and Evans M Harrell II. On the critical exponent in an isoperimetric inequality for chords. 2007. Vol. 368. In Physics Letters A. pp.1-6. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020133149671879731.
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