{
  "id": "2205.02755",
  "version": "v1",
  "published": "2022-05-05T16:31:18.000Z",
  "updated": "2022-05-05T16:31:18.000Z",
  "title": "A lower bound for the logarithmic energy on $\\mathbb{S}^2$ and for the Green energy on $\\mathbb{S}^n$",
  "authors": [
    "Carlos Beltrán",
    "Fátima Lizarte"
  ],
  "comment": "17 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We show an alternative proof of the sharpest known lower bound for the logarithmic energy on the unit sphere $\\mathbb{S}^2$. We then generalize this proof to get new lower bounds for the Green energy on the unit $n$-sphere $\\mathbb{S}^n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-05T16:31:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31C12",
      "31C20",
      "41A60"
    ],
    "keywords": [
      "lower bound",
      "green energy",
      "logarithmic energy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}