{
  "id": "2410.12632",
  "version": "v1",
  "published": "2024-10-16T14:53:13.000Z",
  "updated": "2024-10-16T14:53:13.000Z",
  "title": "An elliptic proof of the splitting theorems from Lorentzian geometry",
  "authors": [
    "Mathias Braun",
    "Nicola Gigli",
    "Robert J. McCann",
    "Argam Ohanyan",
    "Clemens Sämann"
  ],
  "comment": "34 pages",
  "categories": [
    "math.DG",
    "math-ph",
    "math.AP",
    "math.MG",
    "math.MP"
  ],
  "abstract": "We provide a new proof of the splitting theorems from Lorentzian geometry, in which simplicity is gained by sacrificing linearity of the d'Alembertian to recover ellipticity. We exploit a negative homogeneity (non-uniformly) elliptic $p$-d'Alembert operator for this purpose. This allows us to bring the Eschenburg, Galloway, and Newman Lorentzian splitting theorems into a framework closer to the Cheeger-Gromoll splitting theorem from Riemannian geometry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-16T14:53:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "83C75",
      "35J92",
      "35Q75",
      "49Q22",
      "51K10",
      "53C21",
      "53C50",
      "58J05"
    ],
    "keywords": [
      "lorentzian geometry",
      "elliptic proof",
      "newman lorentzian splitting theorems",
      "framework closer",
      "riemannian geometry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}