{
  "id": "2006.07222",
  "version": "v1",
  "published": "2020-06-12T14:27:50.000Z",
  "updated": "2020-06-12T14:27:50.000Z",
  "title": "Cut locus on compact manifolds and uniform semiconcavity estimates for a variational inequality",
  "authors": [
    "François Générau",
    "Edouard Oudet",
    "Bozhidar Velichkov"
  ],
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "We study a family of gradient obstacle problems on a compact Riemannian manifold. We prove that the solutions of these free boundary problems are uniformly semiconcave and, as a consequence, we obtain some fine convergence results for the solutions and their free boundaries. Precisely, we show that the elastic and the $\\lambda$-elastic sets of the solutions Hausdorff converge to the cut locus and the $\\lambda$-cut locus of the manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-12T14:27:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R35",
      "53C21",
      "53C22"
    ],
    "keywords": [
      "cut locus",
      "uniform semiconcavity estimates",
      "variational inequality",
      "compact manifolds",
      "compact riemannian manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}