{
  "id": "1411.2904",
  "version": "v1",
  "published": "2014-11-11T18:00:15.000Z",
  "updated": "2014-11-11T18:00:15.000Z",
  "title": "Isolated singularities of graphs in warped products and Monge-Ampère equations",
  "authors": [
    "José A. Gálvez",
    "Asun Jiménez",
    "Pablo Mira"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We study graphs of positive extrinsic curvature with a non-removable isolated singularity in 3-dimensional warped product spaces, and describe their behavior at the singularity in several natural situations. We use Monge-Amp\\`ere equations to give a classification of the surfaces in 3-dimensional space forms which are embedded around a non-removable isolated singularity and have a prescribed, real analytic, positive extrinsic curvature function at every point. Specifically, we prove that this space is in one-to-one correspondence with the space of regular, analytic, strictly convex Jordan curves in the 2-dimensional sphere $\\mathbb{S^2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-11T18:00:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J96",
      "53C42"
    ],
    "keywords": [
      "warped product",
      "monge-ampère equations",
      "non-removable isolated singularity",
      "positive extrinsic curvature function",
      "strictly convex jordan curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.2904G"
    }
  }
}