{
  "id": "1202.4517",
  "version": "v1",
  "published": "2012-02-21T02:55:15.000Z",
  "updated": "2012-02-21T02:55:15.000Z",
  "title": "The Closure of Spectral Data for Constant Mean Curvature Tori in $ S ^ 3 $",
  "authors": [
    "Emma Carberry",
    "Martin Ulrich Schmidt"
  ],
  "comment": "20 pages",
  "categories": [
    "math.DG",
    "math.AG"
  ],
  "abstract": "The spectral curve correspondence for finite-type solutions of the sinh-Gordon equation describes how they arise from and give rise to hyperelliptic curves with a real structure. Constant mean curvature (CMC) 2-tori in $ S ^ 3 $ result when these spectral curves satisfy periodicity conditions. We prove that the spectral curves of CMC tori are dense in the space of smooth spectral curves of finite-type solutions of the sinh-Gordon equation. One consequence of this is the existence of countably many real $ n $-dimensional families of CMC tori in $ S ^ 3 $ for each positive integer $ n $.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-02-21T02:55:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A10",
      "14H70",
      "53C42",
      "37K10"
    ],
    "keywords": [
      "constant mean curvature tori",
      "spectral data",
      "spectral curves satisfy periodicity conditions",
      "cmc tori",
      "finite-type solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.4517C"
    }
  }
}