{
  "id": "1104.1259",
  "version": "v4",
  "published": "2011-04-07T07:41:45.000Z",
  "updated": "2014-12-14T13:16:30.000Z",
  "title": "New examples of constant mean curvature surfaces in $\\mathbb{S}^2\\times\\mathbb{R}$ and $\\mathbb{H}^2\\times \\mathbb{R}$",
  "authors": [
    "José M. Manzano",
    "Francisco Torralbo"
  ],
  "comment": "22 pages, 5 figures",
  "journal": "Michigan Math. J. 63 (4) (2014), 701-723",
  "doi": "10.1307/mmj/1417799222",
  "categories": [
    "math.DG"
  ],
  "abstract": "We construct non-zero constant mean curvature H surfaces in the product spaces $\\mathbb{S}^2 \\times \\mathbb{R}$ and $\\mathbb{H}^2\\times \\mathbb{R}$ by using suitable conjugate Plateau constructions. The resulting surfaces are complete, have bounded height and are invariant under a discrete group of horizontal translations. In $\\mathbb{S}^2\\times\\mathbb{R}$ (for any $H > 0$) or $\\mathbb{H}^2\\times\\mathbb{R}$ (for $H > 1/2$), a 1-parameter family of unduloid-type surfaces is obtained, some of which are shown to be compact in $\\mathbb{S}^2\\times\\mathbb{R}$. Finally, in the case of $H = 1/2$ in $\\mathbb{H}^2 \\times \\mathbb{R}$, the constructed examples have the symmetries of a tessellation of $\\mathbb{H}^2$ by regular polygons.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-01-24T10:27:10.000Z",
      "title": "New examples of constant mean curvature surfaces in S^2xR and H^2xR",
      "abstract": "We construct non-zero constant mean curvature H surfaces in the product spaces $\\mathbb{S}^2 \\times \\mathbb{R}$ and $\\mathbb{H}^2\\times \\mathbb{R}$ by using suitable conjugate Plateau constructions. The resulting surfaces are complete, have bounded height and are invariant under a discrete group of horizontal translations. In $\\mathbb{S}^2\\times\\mathbb{R}$ (for any H > 0) or $\\mathbb{H}^2\\times\\mathbb{R}$ (for H > 1/2), a 1-parameter family of unduloid-type surfaces is obtained, some of which are shown to be compact in $\\mathbb{S}^2\\times\\mathbb{R}$. Finally, in the case of H = 1/2 in $\\mathbb{H}^2 \\times \\mathbb{R}$, the constructed examples have the symmetries of a tessellation of $\\mathbb{H}^2$ by regular polygons.",
      "comment": "22 pages, 5 figures; 1 figure has been added and the paper has been revised",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-12-14T13:16:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C42",
      "53C30"
    ],
    "keywords": [
      "constant mean curvature surfaces",
      "construct non-zero constant mean curvature",
      "suitable conjugate plateau constructions",
      "product spaces",
      "regular polygons"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.1259M"
    }
  }
}