{
  "id": "1803.01899",
  "version": "v1",
  "published": "2018-03-05T19:49:12.000Z",
  "updated": "2018-03-05T19:49:12.000Z",
  "title": "On the stability of the positive mass theorem for asymptotically hyperbolic graphs",
  "authors": [
    "Armando J. Cabrera Pacheco"
  ],
  "comment": "23 pages, 1 figure",
  "categories": [
    "math.DG",
    "gr-qc"
  ],
  "abstract": "The positive mass theorem states that the total mass of a complete asymptotically flat manifold with non-negative scalar curvature is non-negative; moreover, the total mass equals zero if and only if the manifold is isometric to the Euclidean space. Huang and Lee [2015] proved the stability of the Positive Mass Theorem for a class of $n$-dimensional ($n \\geq 3$) asymptotically flat graphs with non-negative scalar curvature, in the sense of currents. Motivated by their work and using results of Dahl, Gicquaud and Sakovich [2013], we adapt their ideas to obtain a similar result regarding the stability of the positive mass theorem, in the sense of currents, for a class of $n$-dimensional $(n \\geq 3)$ asymptotically hyperbolic graphs with scalar curvature bigger than or equal to $-n(n-1)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-05T19:49:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "83C99",
      "58Z05"
    ],
    "keywords": [
      "asymptotically hyperbolic graphs",
      "non-negative scalar curvature",
      "total mass equals zero",
      "positive mass theorem states",
      "complete asymptotically flat manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}