{
  "id": "2111.05079",
  "version": "v2",
  "published": "2021-11-09T12:19:34.000Z",
  "updated": "2022-09-27T01:22:21.000Z",
  "title": "Scalar curvature lower bound under integral convergence",
  "authors": [
    "Yiqi Huang",
    "Man-Chun Lee"
  ],
  "comment": "final version, 11 pages, minor mistakes corrected",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this work, we consider sequences of $C^2$ metrics which converge to a $C^2$ metric in $C^0$ sense. We show that if the scalar curvature of the sequence is almost non-negative in the integral sense, then the limiting metric has scalar curvature lower bound in point-wise sense.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-09-27T01:22:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "scalar curvature lower bound",
      "integral convergence",
      "integral sense",
      "limiting metric",
      "point-wise sense"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}