{
  "id": "1708.01649",
  "version": "v1",
  "published": "2017-08-04T19:32:55.000Z",
  "updated": "2017-08-04T19:32:55.000Z",
  "title": "Boundary value problems in dimensions seven, four and three related to exceptional holonomy",
  "authors": [
    "Simon Donaldson"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "In the paper we introduce a boundary value problem for a G_{2} structure on a 7-manifold with boundary, with prescribed 3-form on the boundary. We make some general observations about this problem and then study in more detail reductions to 4 and 3 dimensions by imposing symmetry. The 3-dimensional reduction admits a dual variational formulation in terms of solutions of the real Monge-Ampere equation",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-04T19:32:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C26"
    ],
    "keywords": [
      "boundary value problem",
      "dimensions seven",
      "exceptional holonomy",
      "real monge-ampere equation",
      "dual variational formulation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}