{
  "id": "2407.10212",
  "version": "v1",
  "published": "2024-07-14T14:12:39.000Z",
  "updated": "2024-07-14T14:12:39.000Z",
  "title": "Scalar curvature rigidity of domains in a warped product",
  "authors": [
    "Xiaoxiang Chai",
    "Xueyuan Wan"
  ],
  "comment": "32 pages, comments welcome. This preprint supersedes arXiv:2312.16022. A Llarull theorem is added in this paper, and we handle all dimensions; the rigidity of initial data sets would be in a separate paper",
  "categories": [
    "math.DG"
  ],
  "abstract": "By exploiting the conformality of a warped product metric with a direct product metric, we develop a new connection on a twisted spinor bundle and its associated Dirac operator. We obtain a Llarull type scalar curvature rigidity for a general class of domains in a warped product. Also, we are able to address Gromov dihedral rigidity in hyperbolic space assuming matching angles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-14T14:12:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C24",
      "53C27",
      "53C21"
    ],
    "keywords": [
      "warped product",
      "llarull type scalar curvature rigidity",
      "address gromov dihedral rigidity",
      "hyperbolic space assuming matching angles",
      "direct product metric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}