{
  "id": "2309.13372",
  "version": "v1",
  "published": "2023-09-23T13:20:59.000Z",
  "updated": "2023-09-23T13:20:59.000Z",
  "title": "Conservation law of harmonic mappings in supercritical dimensions",
  "authors": [
    "Chang-Yu Guo",
    "Chang-Lin Xiang"
  ],
  "comment": "6 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "In this short note, we provide a partial extension of Rivi\\`ere's convervation law in higher dimensions under certain Lorentz integrability condition for the connection matrix. As an application, we obtain a conservation law for weakly harmonic mappings around regular points in supercritical dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-23T13:20:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E20",
      "35J60"
    ],
    "keywords": [
      "conservation law",
      "supercritical dimensions",
      "lorentz integrability condition",
      "convervation law",
      "short note"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}