{
  "id": "2009.01050",
  "version": "v1",
  "published": "2020-09-02T13:24:57.000Z",
  "updated": "2020-09-02T13:24:57.000Z",
  "title": "The strong $L^p$-closure of vector fields with finitely many integer singularities on $B^3$",
  "authors": [
    "Riccardo Caniato"
  ],
  "categories": [
    "math.FA",
    "math.AP",
    "math.DG"
  ],
  "abstract": "This paper is aimed to investigate the strong $L^p$-closure $L_{\\mathbb{Z}}^p(B)$ of the vector fields on the open unit ball $B\\subset\\mathbb{R}^3$ that are smooth up to finitely many integer point singularities. First, such strong closure is characterized for arbitrary $p\\in[1,+\\infty)$. Secondly, it is shown what happens if the integrability order $p$ is large enough (namely, if $p\\ge 3/2$). Eventually, a decomposition theorem for elements in $L_{\\mathbb{Z}}^1(B)$ is given, conveying information about the possibility of connecting the singular set of such vector fields by an integer $1$-current on $B$ with finite mass.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-02T13:24:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vector fields",
      "integer singularities",
      "open unit ball",
      "integer point singularities",
      "strong closure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}