{
  "id": "1907.06395",
  "version": "v1",
  "published": "2019-07-15T09:45:05.000Z",
  "updated": "2019-07-15T09:45:05.000Z",
  "title": "Lifting for manifold-valued maps of bounded variation",
  "authors": [
    "Giacomo Canevari",
    "Giandomenico Orlandi"
  ],
  "comment": "15 pages, 2 figures",
  "categories": [
    "math.FA",
    "math.AP"
  ],
  "abstract": "Let $\\mathcal{N}$ be a smooth, compact, connected Riemannian manifold without boundary. Let $\\mathcal{E}\\to\\mathcal{N}$ be the Riemannian universal covering of $\\mathcal{N}$. For any bounded, smooth domain $\\Omega\\subseteq\\mathbb{R}^d$ and any $u\\in\\mathrm{BV}(\\Omega, \\, \\mathcal{N})$, we show that $u$ has a lifting $v\\in\\mathrm{BV}(\\Omega, \\, \\mathcal{E})$. Our result proves a conjecture by Bethuel and Chiron.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-15T09:45:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded variation",
      "manifold-valued maps",
      "smooth domain",
      "connected riemannian manifold",
      "riemannian universal covering"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}