{
  "id": "math/0310397",
  "version": "v2",
  "published": "2003-10-24T21:49:51.000Z",
  "updated": "2004-10-01T12:35:19.000Z",
  "title": "Towards a classification of CMC-1 Trinoids in hyperbolic space via conjugate surfaces",
  "authors": [
    "Andreas Balser"
  ],
  "comment": "14 pages, 1 figure; presentation improved and shortened",
  "categories": [
    "math.DG"
  ],
  "abstract": "We derive necessary conditions on the parameters of the ends of a CMC-1 trinoid in hyperbolic 3-space $H^{3}$ with symmetry plane by passing to its conjugate minimal surface. Together with Daniel's results, this yields a classification of generic symmetric trinoids. We also discuss the relation to other classification results of trinoids by Bobenko et al. and Umehara-Yamada. To obtain the result above, we show that the conjugate minimal surface of a catenoidal CMC-1 end in $H^{3}$ with symmetry plane is asymptotic to a suitable helicoid.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-10-01T12:35:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A10",
      "53C42"
    ],
    "keywords": [
      "hyperbolic space",
      "conjugate surfaces",
      "conjugate minimal surface",
      "symmetry plane",
      "generic symmetric trinoids"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....10397B"
    }
  }
}