{
  "id": "2405.09750",
  "version": "v1",
  "published": "2024-05-16T01:20:04.000Z",
  "updated": "2024-05-16T01:20:04.000Z",
  "title": "Scalar curvature lower bounds on asymptotically flat manifolds",
  "authors": [
    "Yuqiao Li"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we consider the scalar curvature in the distributional sense of \\cite{MR3366052} and the scalar curvature lower bound in the $\\beta-$weak $(\\beta\\in(0, \\frac{1}{2}))$ sense of \\cite{MR4685089} on an asymptotically flat $n-$manifold with a $W^{1,p}(p>n)$ metric. We first show that the scalar curvature lower bound under the Ricci-DeTurck flow depends on the scalar curvature lower bound in the $\\beta-$weak sense and the time. Then we prove that the lower bound of the distributional scalar curvature of a $W^{1, p}$ metric coincides with the lower bound of the scalar curvature in the $\\beta-$weak sense at infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-16T01:20:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "scalar curvature lower bound",
      "asymptotically flat manifolds",
      "weak sense",
      "distributional scalar curvature",
      "ricci-deturck flow"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}