{
  "id": "1110.5357",
  "version": "v4",
  "published": "2011-10-24T21:21:02.000Z",
  "updated": "2011-12-07T09:10:07.000Z",
  "title": "On conformal surfaces of annulus type",
  "authors": [
    "Yong Luo"
  ],
  "comment": "Some typos have been polished and I find that the best constant for L^infinity norm in Wente inequality has been established by Topping in a paper dated to 1997",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "Let $a>b>0$ and $f$ be a conformal map from $B_a\\setminus B_b\\subseteq R^2$ into $\\R^n$, with $|\\nabla f|^2=2e^{2u}$. Then $(e_1, e_2)$ with $e_1=e^{-u}\\frac{\\partial f}{\\partial r},$ and $e_2=r^{-1}e^{-u}\\frac{\\partial f}{\\partial\\theta}$ is a moving frame on $f(B_a\\setminus B_b)$. It satisfies the following equation $$d\\star<de_1, e_2>=0,$$ where $\\star$ is the Hodge star operator on $R^2$ with respect to the standard metric. We will study the Dirichret energy of this frame and give some applications.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-12-07T09:10:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "annulus type",
      "conformal surfaces",
      "hodge star operator",
      "dirichret energy",
      "standard metric"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.jde.2012.08.036",
      "journal": "Journal of Differential Equations",
      "year": 2012,
      "volume": 253,
      "number": 12,
      "pages": 3266
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JDE...253.3266L"
    }
  }
}