{
  "id": "1704.08673",
  "version": "v1",
  "published": "2017-04-27T17:36:10.000Z",
  "updated": "2017-04-27T17:36:10.000Z",
  "title": "Partial regularity of harmonic maps from a Riemannian manifold into a Lorentzian manifold",
  "authors": [
    "Jiayu Li",
    "Lei Liu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we will study the partial regularity theorem for stationary harmonic maps from a Riemannian manifold into a Lorentzian manifold. For a weakly stationary harmonic map $(u,v)$ from a smooth bounded open domain $\\Omega\\subset\\R^m$ to a Lorentzian manifold with Dirichlet boundary condition, we prove that it is smooth outside a closed set whose $(m-2)$-dimension Hausdorff measure is zero. Moreover, if the target manifold $N$ does not admit any harmonic sphere $S^l$, $l=2,...,m-1$, we will show $(u,v)$ is smooth.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-27T17:36:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lorentzian manifold",
      "riemannian manifold",
      "weakly stationary harmonic map",
      "dimension hausdorff measure",
      "smooth bounded open domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}