{
  "id": "2505.10520",
  "version": "v1",
  "published": "2025-05-15T17:29:18.000Z",
  "updated": "2025-05-15T17:29:18.000Z",
  "title": "Sharp integral bound of scalar curvature on $3$-manifolds",
  "authors": [
    "Ovidiu Munteanu",
    "Jiaping Wang"
  ],
  "comment": "21 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "It is shown that the integral of the scalar curvature on a geodesic ball of radius $R$ in a three-dimensional complete manifold with nonnegative Ricci curvature is bounded above by $8\\pi R$ asymptotically for large $R$ provided that the scalar curvature is bounded between two positive constants.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-15T17:29:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "scalar curvature",
      "sharp integral bound",
      "three-dimensional complete manifold",
      "nonnegative ricci curvature",
      "geodesic ball"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}