{
  "id": "1002.4805",
  "version": "v3",
  "published": "2010-02-25T14:55:36.000Z",
  "updated": "2010-03-12T17:03:24.000Z",
  "title": "Construction of Triply Periodic Minimal Surfaces",
  "authors": [
    "Rami Younes"
  ],
  "comment": "The paper has been removed so that it could be uploaded correctly!",
  "categories": [
    "math.DG"
  ],
  "abstract": "Given a tiling $\\mathcal{T}$ of the plane by straight edge polygons, which is invariant by two independent translations, we construct a family of embedded triply periodic minimal surfaces which desingularizes $\\mathcal{T}\\times\\mathbb{R}$. For this purpose, inspired by the work of Martin Traizet, we open the nodes of singular Riemann surfaces to glue together simply periodic Karcher saddle towers, each placed at a vertex of the tiling in such a way that its wings go along the corresponding edges of the tiling ending at that vertex.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-03-12T17:03:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A10"
    ],
    "keywords": [
      "construction",
      "simply periodic karcher saddle towers",
      "singular riemann surfaces",
      "embedded triply periodic minimal surfaces",
      "straight edge polygons"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.4805Y"
    }
  }
}