{
  "id": "1208.1470",
  "version": "v2",
  "published": "2012-08-07T17:10:17.000Z",
  "updated": "2012-09-24T16:22:22.000Z",
  "title": "On uniqueness of heat flow of harmonic maps",
  "authors": [
    "Tao Huang",
    "Changyou Wang"
  ],
  "comment": "24 pages. Two errors of proof of lemma 2.3 have been fixed",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "In this paper, we establish the uniqueness of heat flow of harmonic maps into (N, h) that have sufficiently small renormalized energies, provided that N is either a unit sphere $S^{k-1}$ or a compact Riemannian homogeneous manifold without boundary. For such a class of solutions, we also establish the convexity property of the Dirichlet energy for $t\\ge t_0>0$ and the unique limit property at time infi?nity. As a corollary, the uniqueness is shown for heat flow of harmonic maps into any compact Riemannian manifold N without boundary whose gradients belong to $L^q_t L^l_x$ for $q>2$ and $l>n$ satisfying the Serrin's condition.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-24T16:22:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "53C44"
    ],
    "keywords": [
      "harmonic maps",
      "heat flow",
      "uniqueness",
      "compact riemannian homogeneous manifold",
      "unique limit property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.1470H"
    }
  }
}