{
  "id": "1512.01153",
  "version": "v1",
  "published": "2015-12-03T16:46:26.000Z",
  "updated": "2015-12-03T16:46:26.000Z",
  "title": "A Feynman-Kac formula for differential forms on manifolds with boundary and applications",
  "authors": [
    "Levi Lopes de Lima"
  ],
  "comment": "20 pages; no figures",
  "categories": [
    "math.DG",
    "math.PR"
  ],
  "abstract": "We prove a Feynman-Kac formula for differential forms satisfying absolute boundary conditions on Riemannian manifolds with boundary and of bounded geometry. We use this to construct $L^2$ harmonic forms out of bounded ones on the universal cover of a compact Riemannian manifold whose geometry displays a positivity property expressed in terms of a certain stochastic average of the Weitzenb\\\"ock operator $R_p$ acting on $p$-forms and the second fundamental form of the boundary. This extends previous work by Elworthy-Li-Rosenberg on closed manifolds to this setting. As an application we find a geometric obstruction to the existence of metrics with 2-convex boundary and positive $R_2$ in this stochastic sense. We also discuss a version of the Feynman-Kac formula for spinors under suitable boundary conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-03T16:46:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21",
      "53C27",
      "58J35",
      "58J65"
    ],
    "keywords": [
      "feynman-kac formula",
      "application",
      "forms satisfying absolute boundary conditions",
      "differential forms satisfying absolute boundary",
      "second fundamental form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151201153L"
    }
  }
}