{
  "id": "2003.05595",
  "version": "v1",
  "published": "2020-03-12T03:22:25.000Z",
  "updated": "2020-03-12T03:22:25.000Z",
  "title": "Optimal regularity for the Pfaff system and isometric immersions in arbitrary dimensions",
  "authors": [
    "Siran Li"
  ],
  "comment": "10 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We prove the existence, uniqueness, and $W^{1,2}$-regularity for the solution to the Pfaff system with antisymmetric $L^2$-coefficient matrix in arbitrary dimensions. Hence, we establish the equivalence between the existence of $W^{2,2}$-isometric immersions and the weak solubility of the Gauss--Codazzi--Ricci equations on simply-connected domains. The regularity assumptions of these results are sharp.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-12T03:22:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58A17",
      "58A15",
      "53A07",
      "53C42",
      "35M30",
      "58J60"
    ],
    "keywords": [
      "isometric immersions",
      "pfaff system",
      "arbitrary dimensions",
      "optimal regularity",
      "coefficient matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}