{
  "id": "1206.1184",
  "version": "v3",
  "published": "2012-06-06T11:15:07.000Z",
  "updated": "2015-08-06T00:23:15.000Z",
  "title": "Convergence of scalar-flat metrics on manifolds with boundary under a Yamabe-type flow",
  "authors": [
    "Sergio Almaraz"
  ],
  "comment": "Title slightly changed. Introduction improved and changed to include the recent results (arXiv:1407.0673) on Conjecture 1.5. Appendix C removed and published as a separate paper (arXiv:1508.01058). Although Appendix B was shortened for publication, this arxiv version remains complete and unchanged. Some typos corrected. 71 pages",
  "journal": "Journal of Differential Equations, 259 (2015) 2626-2694",
  "doi": "10.1016/j.jde.2015.04.011",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We study a conformal flow for compact Riemannian manifolds of dimension greater than two with boundary. Convergence to a scalar-flat metric with constant mean curvature on the boundary is established in dimensions up to seven, and in any dimensions if the manifold is spin or if it satisfies a generic condition.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-06T17:00:16.000Z",
      "title": "Convergence of scalar-flat metrics on manifolds with boundary under the Yamabe flow",
      "abstract": "This paper is concerned with a Yamabe-type flow for compact Riemannian manifolds with boundary. The convergence of this flow is established if the manifold with boundary satisfies either a generic condition or a positive mass theorem.",
      "comment": "Some typos correted, including the formulas (3.4),(C-6), the 1st formula on p.16, and (P1, P2) of Proposition B-2. Some changes in Section 2 to show independence of the sign of H_{g(0)}. Presentantion of Appendix C improved and references added",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-08-06T00:23:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J65",
      "53C25"
    ],
    "keywords": [
      "scalar-flat metrics",
      "yamabe flow",
      "convergence",
      "compact riemannian manifolds",
      "yamabe-type flow"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 71,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.1184A"
    }
  }
}