{
  "id": "1912.04863",
  "version": "v1",
  "published": "2019-12-10T18:07:23.000Z",
  "updated": "2019-12-10T18:07:23.000Z",
  "title": "Singularities of solutions of time dependent Hamilton-Jacobi equations. Applications to Riemannian geometry",
  "authors": [
    "Piermarco Cannarsa",
    "Wei Cheng",
    "Albert Fathi"
  ],
  "categories": [
    "math.AP",
    "math.DG",
    "math.OC"
  ],
  "abstract": "If $U:[0,+\\infty[\\times M$ is a uniformly continuous viscosity solution of the evolution Hamilton-Jacobi equation $$\\partial_tU+ H(x,\\partial_xU)=0,$$ where $M$ is a not necessarily compact manifold, and $H$ is a Tonelli Hamiltonian, we prove the set $\\Sigma(U)$, of points where $U$ is not differentiable, is locally contractible. Moreover, we study the homotopy type of $\\Sigma(U)$. We also give an application to the singularities of a distance function to a closed subset of a complete Riemannian manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-10T18:07:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35F21",
      "35D40",
      "49C05",
      "58J47"
    ],
    "keywords": [
      "time dependent hamilton-jacobi equations",
      "riemannian geometry",
      "singularities",
      "application",
      "evolution hamilton-jacobi equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}