{
  "id": "1903.00916",
  "version": "v1",
  "published": "2019-03-03T14:11:38.000Z",
  "updated": "2019-03-03T14:11:38.000Z",
  "title": "Lower semicontinuity of ADM mass under intrinsic flat convergence",
  "authors": [
    "Jeffrey L. Jauregui",
    "Dan A. Lee"
  ],
  "comment": "42 pages, 3 figures",
  "categories": [
    "math.DG",
    "gr-qc"
  ],
  "abstract": "A natural question in mathematical general relativity is how the ADM mass behaves as a functional on the space of asymptotically flat 3-manifolds of nonnegative scalar curvature. In previous results, lower semicontinuity has been established by the first-named author for pointed $C^2$ convergence, and more generally by both authors for pointed $C^0$ convergence (all in the Cheeger--Gromov sense). In this paper, we show this behavior persists for the much weaker notion of pointed Sormani--Wenger intrinsic flat ($\\mathcal{F}$) volume convergence, under natural hypotheses. We consider smooth manifolds converging to asymptotically flat local integral current spaces (a new definition), using Huisken's isoperimetric mass as a replacement for the ADM mass. Along the way we prove results of independent interest about convergence of subregions of $\\mathcal{F}$-converging sequences of integral current spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-03T14:11:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "83C99",
      "58Z05"
    ],
    "keywords": [
      "intrinsic flat convergence",
      "adm mass",
      "lower semicontinuity",
      "flat local integral current spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}