{
  "id": "2206.09768",
  "version": "v1",
  "published": "2022-06-20T13:30:32.000Z",
  "updated": "2022-06-20T13:30:32.000Z",
  "title": "Rigidity of non-compact static domains in hyperbolic space via positive mass theorems",
  "authors": [
    "Sergio Almaraz",
    "Levi Lopes de Lima"
  ],
  "comment": "28 pages, no figures",
  "categories": [
    "math.DG",
    "gr-qc"
  ],
  "abstract": "We single out a notion of staticity which applies to any domain in hyperbolic space whose boundary is a non-compact totally umbilical hypersurface. For (time-symmetric) initial data sets modeled at infinity on any of these latter examples, we formulate and prove a positive mass theorem in the spin category under natural dominant energy conditions (both in the interior and along the boundary) whose rigidity statement retrieves, among other things, a sharper version of a recent result by Souam to the effect that no such hypersurface admits a compactly supported deformation keeping the original lower bound on the mean curvature. A key ingredient in our approach is the consideration of a family of elliptic boundary conditions on spinors interpolating between chirality and MIT bag boundary conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-20T13:30:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive mass theorem",
      "non-compact static domains",
      "hyperbolic space",
      "natural dominant energy conditions",
      "mit bag boundary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}