{
  "id": "1211.3645",
  "version": "v2",
  "published": "2012-11-15T16:31:33.000Z",
  "updated": "2013-04-29T06:51:11.000Z",
  "title": "A new mass for asymptotically flat manifolds",
  "authors": [
    "Yuxin Ge",
    "Guofang Wang",
    "Jie Wu"
  ],
  "comment": "32 pages. arXiv:1211.7305 was integrated into this new version as an application",
  "categories": [
    "math.DG",
    "gr-qc"
  ],
  "abstract": "In this paper we introduce a mass for asymptotically flat manifolds by using the Gauss-Bonnet curvature. We first prove that the mass is well-defined and is a geometric invariant, if the Gauss-Bonnet curvature is integrable and the decay order $\\tau$ satisfies $\\tau > \\frac {n-4}{3}.$ Then we show a positive mass theorem for asymptotically flat graphs over ${\\mathbb R}^n$. Moreover we obtain also Penrose type inequalities in this case.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-29T06:51:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotically flat manifolds",
      "gauss-bonnet curvature",
      "penrose type inequalities",
      "decay order",
      "geometric invariant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1203215,
      "adsabs": "2012arXiv1211.3645G"
    }
  }
}