{
  "id": "2404.17533",
  "version": "v1",
  "published": "2024-04-26T16:57:52.000Z",
  "updated": "2024-04-26T16:57:52.000Z",
  "title": "Rigidity of spin fill-ins with non-negative scalar curvature",
  "authors": [
    "Simone Cecchini",
    "Sven Hirsch",
    "Rudolf Zeidler"
  ],
  "comment": "20 pages",
  "categories": [
    "math.DG",
    "gr-qc"
  ],
  "abstract": "We establish new mean curvature rigidity theorems of spin fill-ins with non-negative scalar curvature using two different spinorial techniques. Our results address two questions by Miao and Gromov, respectively. The first technique is based on extending boundary spinors satisfying a generalized eigenvalue equation via the Fredholm alternative for an APS boundary value problem, while the second is a comparison result in the spirit of Llarull and Lott using index theory. We also show that the latter implies a new Witten-type integral inequality for the mass of an asymptotically Schwarzschild manifold which holds even when the scalar curvature is not assumed to be non-negative.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-26T16:57:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-negative scalar curvature",
      "spin fill-ins",
      "mean curvature rigidity theorems",
      "aps boundary value problem",
      "witten-type integral inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}