{
  "id": "math/0703197",
  "version": "v1",
  "published": "2007-03-07T14:08:18.000Z",
  "updated": "2007-03-07T14:08:18.000Z",
  "title": "Green functions for the Dirac operator under local boundary conditions and applications",
  "authors": [
    "Simon Raulot"
  ],
  "comment": "23 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we define the Green function for the Dirac operator under two local boundary conditions: the condition associated with a chirality operator (also called the chiral bag boundary condition) and the $\\MIT$ bag boundary condition. Then we give some applications of these constructions for each Green function. From the existence of the chiral Green function, we derive an inequality on a spin conformal invariant which, in particular, solve the Yamabe problem on manifolds with boundary in some cases. Finally, using the $\\MIT$ Green function, we give a simple proof of a positive mass theorem previously proved by Escobar.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-07T14:08:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A30",
      "53C27",
      "58J50",
      "58C40"
    ],
    "keywords": [
      "local boundary conditions",
      "dirac operator",
      "applications",
      "chiral bag boundary condition",
      "chiral green function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3197R"
    }
  }
}