{
  "id": "2101.10023",
  "version": "v1",
  "published": "2021-01-25T11:48:31.000Z",
  "updated": "2021-01-25T11:48:31.000Z",
  "title": "On a Conjecture of Bahri-Xu",
  "authors": [
    "Hong Chen",
    "Jianquan Ge",
    "Kai Jia",
    "Zhiqin Lu"
  ],
  "comment": "Accepted by Acta Math. Sin. (Engl. Ser.)",
  "categories": [
    "math.CA",
    "math.DG",
    "math.SP"
  ],
  "abstract": "In order to study the Yamabe changing-sign problem, Bahri and Xu proposed a conjecture which is a universal inequality for $p$ points in $\\mathbb R^m$. They have verified the conjecture for $p\\leq3$. In this paper, we first simplify this conjecture by giving two sufficient and necessary conditions inductively. Then we prove the conjecture for the basic case $m=1$ with arbitrary $p$. In addition, for the cases when $p=4,5$ and $m\\geq2$, we manage to reduce them to the basic case $m=1$ and thus prove them as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-25T11:48:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conjecture",
      "basic case",
      "yamabe changing-sign problem",
      "universal inequality",
      "necessary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}