{
  "id": "0912.5081",
  "version": "v2",
  "published": "2009-12-30T05:18:48.000Z",
  "updated": "2010-08-30T16:31:22.000Z",
  "title": "Singularities of spacelike constant mean curvature surfaces in Lorentz-Minkowski space",
  "authors": [
    "David Brander"
  ],
  "comment": "28 pages, 2 figures. Version 2: Figure 2 added",
  "journal": "Math. Proc. Camb. Phil. Soc. (2011), 150, 527--556",
  "doi": "10.1017/S030500411100007",
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study singularities of spacelike, constant (non-zero) mean curvature (CMC) surfaces in the Lorentz-Minkowski 3-space $L^3$. We show how to solve the singular Bj\\\"orling problem for such surfaces, which is stated as follows: given a real analytic null-curve $f_0(x)$, and a real analytic null vector field $v(x)$ parallel to the tangent field of $f_0$, find a conformally parameterized (generalized) CMC $H$ surface in $L^3$ which contains this curve as a singular set and such that the partial derivatives $f_x$ and $f_y$ are given by $\\frac{\\dd f_0}{\\dd x}$ and $v$ along the curve. Within the class of generalized surfaces considered, the solution is unique and we give a formula for the generalized Weierstrass data for this surface. This gives a framework for studying the singularities of non-maximal CMC surfaces in $L^3$. We use this to find the Bj\\\"orling data -- and holomorphic potentials -- which characterize cuspidal edge, swallowtail and cross cap singularities.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-08-30T16:31:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A10",
      "53C42",
      "53A35"
    ],
    "keywords": [
      "spacelike constant mean curvature surfaces",
      "lorentz-minkowski space",
      "singularities",
      "real analytic null vector field"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.5081B"
    }
  }
}