{
  "id": "0912.1302",
  "version": "v2",
  "published": "2009-12-07T18:40:11.000Z",
  "updated": "2010-04-08T15:41:56.000Z",
  "title": "Conformal Deformation to Scalar Flat Metrics with Constant Mean Curvature on the Boundary in Higher Dimensions",
  "authors": [
    "Szu-yu Sophie Chen"
  ],
  "comment": "27 pages, title changed, introduction expanded",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In 1992, motivated by Riemann mapping theorem, Escobar considered a version of Yamabe problem on manifolds of dimension n greater than 2 with boundary. The problem consists in finding a conformal metric such that the scalar curvature is zero and the mean curvature is constant on the boundary. By using a local test function construction, we are able to seattle the most cases left by Escobar's and Marques's works. Moreover, we reduce the remaining case to the positive mass theorem. In this proof, we use the method developed in previous works by Brendle and by Brendle and the author.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-04-08T15:41:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "constant mean curvature",
      "scalar flat metrics",
      "conformal deformation",
      "higher dimensions",
      "local test function construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.1302C"
    }
  }
}