{
  "id": "1306.0219",
  "version": "v1",
  "published": "2013-06-02T15:29:22.000Z",
  "updated": "2013-06-02T15:29:22.000Z",
  "title": "Constant mean curvature $k$-noids in homogeneous manifolds",
  "authors": [
    "Julia Plehnert"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "For each $k\\geq2$, we construct two families of surfaces with constant mean curvature $H$ for $H\\in[0,1/2]$ in $\\Sigma(\\kappa)\\times\\R$ where $\\kappa+4H^2\\leq0$. The surfaces are invariant under $2\\pi/k$-rotations about a vertical fiber of $\\Sigma(\\kappa)\\times\\R$, have genus zero, and a finite number of ends. The first family generalizes the notion of $k$-noids: It has $k$ ends, one horizontal and $k$ vertical symmetry planes. The second family is less symmetric and has two types of ends. Each surface arises as the conjugate (sister) surface of a minimal graph in a homogeneous 3-manifold. The domain of the graph is non-convex in the second family. For $\\kappa=-1$ the surfaces with constant mean curvature $H$ arise from a minimal surface in $\\widetilde{\\PSL}_2(\\R)$ for $H\\in(0,1/2)$ and in $\\Nil$ for H=1/2. For H=0, the conjugate surfaces are both minimal in a product space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-02T15:29:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "constant mean curvature",
      "homogeneous manifolds",
      "genus zero",
      "vertical symmetry planes",
      "second family"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.0219P"
    }
  }
}