{
  "id": "1309.4278",
  "version": "v2",
  "published": "2013-09-17T12:17:33.000Z",
  "updated": "2015-04-09T10:49:18.000Z",
  "title": "Mean-convex Alexandrov embedded constant mean curvature tori in the 3-sphere",
  "authors": [
    "L. Hauswirth",
    "M. Kilian",
    "M. U. Schmidt"
  ],
  "comment": "This is a revised version of arXiv:0712.0108",
  "categories": [
    "math.DG"
  ],
  "abstract": "We introduce the moduli space of spectral curves of constant mean curvature (\\cmc\\hspace{-5pt}) cylinders of finite type in the round unit 3-sphere. The subset of spectral curves of mean-convex Alexandrov embedded cylinders is explicitly determined using a combination of integrable systems and geometric analysis techniques. We prove that these cylinders are surfaces of revolution. As a consequence all mean-convex Alexandrov embedded {\\sc{cmc}} tori in the 3-sphere are surfaces of revolution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-17T12:17:33.000Z",
      "title": "The geometry of embedded constant mean curvature tori in the 3-sphere via integrable systems",
      "abstract": "We introduce the moduli space of spectral curves of constant mean curvature cylinders of finite type in the 3-sphere. Moduli space parameters are a hyperelliptic Riemann surface and a meromorphic one form. The subset of spectral curves of mean convex Alexandrov embedded cylinders is explicitly determined. We prove that all embedded constant mean curvature tori in the 3-sphere are surfaces of revolution using a combination of integrable systems methods and geometric analysis techniques.",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-04-09T10:49:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A10",
      "37K10"
    ],
    "keywords": [
      "embedded constant mean curvature tori",
      "integrable systems",
      "spectral curves",
      "constant mean curvature cylinders",
      "mean convex alexandrov embedded cylinders"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.4278H"
    }
  }
}