三角双锥极小化一类幂律势

Richard Evan Schwartz

三角双锥极小化一类幂律势

度量几何 2016-08-19 v3

作者: Richard Evan Schwartz

摘要

结合A. Tumanov的巧妙观测与我们针对Thomson五电子问题的计算方法，我们证明在单位球面上所有5点构型中，三角双锥是Riesz势 $R_s(r) = \mathrm{sign}(s) r^{-s}$ 的唯一全局极小化子，只要 $s \in (-2,0)$ 或 $s \in (0,13]$ 。下界是锐的，上界非常接近假定的锐截止约15.040908。我希望在后续论文中达到锐 cutoff。本文的讨论部分简要勾勒了将在后续处理指数范围 $[13,15.04.0809...]$ 的方法。

关键词

三角双锥幂律势 Riesz势 Thomson问题全局极小化子单位球面五点构型

引用

@article{arxiv.1512.04628,
  title  = {The Triangular Bi-Pyramid Minimizes a Range of Power Law Potentials},
  author = {Richard Evan Schwartz},
  journal= {arXiv preprint arXiv:1512.04628},
  year   = {2016}
}

备注

An extensive computer program, with a graphical user interface, is available from my website. The paper has instructions on how to download and run it. This version is an improvement over the previous version. The results are better and the second half of the proof is somewhat cleaner

三角双锥极小化一类幂律势

摘要

关键词

引用

备注

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