{
  "id": "1303.0628",
  "version": "v1",
  "published": "2013-03-04T07:50:16.000Z",
  "updated": "2013-03-04T07:50:16.000Z",
  "title": "The Yang-Mills α-flow in vector bundles over four manifolds and its applications",
  "authors": [
    "Min-Chun Hong",
    "Gang Tian",
    "Hao Yin"
  ],
  "comment": "36 pages",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this paper, we introduce an \\alpha -flow for the Yang-Mills functional in vector bundles over four dimensional Riemannian manifolds, and establish global existence of a unique smooth solution to the \\alpha -flow with smooth initial value. We prove that the limit of solutions of the \\alpha -flow as \\alpha\\to 1 is a weak solution to the Yang-Mills flow. By an application of the \\alpha -flow, we then follow the idea of Sacks and Uhlenbeck to prove some existence results for Yang-Mills connections and improve the minimizing result of the Yang-Mills functional of Sedlacek.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-04T07:50:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E15"
    ],
    "keywords": [
      "vector bundles",
      "application",
      "yang-mills functional",
      "unique smooth solution",
      "smooth initial value"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1222393,
      "adsabs": "2013arXiv1303.0628H"
    }
  }
}