{
  "id": "1901.00901",
  "version": "v1",
  "published": "2019-01-03T20:12:54.000Z",
  "updated": "2019-01-03T20:12:54.000Z",
  "title": "Global existence of the harmonic map heat flow into Lorentzian manifolds",
  "authors": [
    "Xiaoli Han",
    "Juergen Jost",
    "Lei Liu",
    "Liang Zhao"
  ],
  "comment": "to appear in J. Math. Pures Appl",
  "categories": [
    "math.DG"
  ],
  "abstract": "We investigate a parabolic-elliptic system for maps $(u,v)$ from a compact Riemann surface $M$ into a Lorentzian manifold $N\\times{\\mathbb{R}}$ with a warped product metric. That system turns the harmonic map type equations into a parabolic system, but keeps the $v$-equation as a nonlinear second order constraint along the flow. We prove a global existence result of the parabolic-elliptic system by assuming either some geometric conditions on the target Lorentzian manifold or small energy of the initial maps. The result implies the existence of a Lorentzian harmonic map in a given homotopy class with fixed boundary data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-03T20:12:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harmonic map heat flow",
      "global existence",
      "nonlinear second order constraint",
      "parabolic-elliptic system",
      "harmonic map type equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}