{
  "id": "1504.02544",
  "version": "v1",
  "published": "2015-04-10T03:38:12.000Z",
  "updated": "2015-04-10T03:38:12.000Z",
  "title": "Log-optimal configurations on the sphere",
  "authors": [
    "P. D. Dragnev"
  ],
  "comment": "15 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this article we consider the distribution of $N$ points on the unit sphere $\\mathbb{S}^{d-1}$ in $\\mathbb{R}^d$ interacting via logarithmic potential. A characterization theorem of the stationary configurations is derived when $N=d+2$ and two new log-optimal configurations minimizing the logarithmic energy are obtained for six points on $\\mathbb{S}^3$ and seven points on $\\mathbb{S}^4$. A conjecture on the log-optimal configurations of $d+2$ points on $\\mathbb{S}^{d-1}$ is stated and three auxiliary results supporting the conjecture are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-10T03:38:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "74G05",
      "74G65",
      "31B15",
      "31C15"
    ],
    "keywords": [
      "conjecture",
      "characterization theorem",
      "seven points",
      "unit sphere",
      "logarithmic potential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150402544D"
    }
  }
}