{
  "id": "1610.01649",
  "version": "v1",
  "published": "2016-10-01T23:31:26.000Z",
  "updated": "2016-10-01T23:31:26.000Z",
  "title": "Compensated Compactness in Banach Spaces and Weak Rigidity of Isometric Immersions of Manifolds",
  "authors": [
    "Gui-Qiang G. Chen",
    "Siran Li"
  ],
  "comment": "22 pages",
  "categories": [
    "math.DG",
    "math.AP",
    "math.FA"
  ],
  "abstract": "We present a compensated compactness theorem in Banach spaces established recently, whose formulation is originally motivated by the weak rigidity problem for isometric immersions of manifolds with lower regularity. As a corollary, a geometrically intrinsic div-curl lemma for tensor fields on Riemannian manifolds is obtained. Then we show how this intrinsic div-curl lemma can be employed to establish the global weak rigidity of the Gauss-Codazzi-Ricci equations, the Cartan formalism, and the corresponding isometric immersions of Riemannian submanifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-01T23:31:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C24",
      "53C42",
      "53C21",
      "53C45",
      "57R42",
      "35M30",
      "35B35",
      "58A15",
      "58J10",
      "57R40",
      "58A14",
      "58A17",
      "58A05",
      "58K30",
      "58Z05"
    ],
    "keywords": [
      "isometric immersions",
      "banach spaces",
      "compensated compactness",
      "geometrically intrinsic div-curl lemma",
      "weak rigidity problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}