{
  "id": "math/0407153",
  "version": "v3",
  "published": "2004-07-09T00:04:04.000Z",
  "updated": "2005-06-22T15:39:24.000Z",
  "title": "On the nondegeneracy of constant mean curvature surfaces",
  "authors": [
    "Nick Korevaar",
    "Rob Kusner",
    "Jesse Ratzkin"
  ],
  "comment": "v2: substantial revisions, to appear in Geom. Funct. Anal.; three figures",
  "journal": "Geom. Funct. Anal. 16 (2006), 891-923",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We prove that many complete, noncompact, constant mean curvature (CMC) surfaces $f:\\Sigma \\to \\R^3$ are nondegenerate; that is, the Jacobi operator $\\Delta_f + |A_f|^2$ has no $L^2$ kernel. In fact, if $\\Sigma$ has genus zero and $f(\\Sigma)$ is contained in a half-space, then we find an explicit upper bound for the dimension of the $L^2$ jernel in terms of the number of non-cylindrical ends. Our main tool is a conjugation operation on Jacobi fields which linearizes the conjugate cousin construction. Consequences include partial regularity for CMC moduli space, a larger class of CMC surfaces to use in gluing constructions, and a surprising characterization of CMC surfaces via spinning spheres.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-06-22T15:39:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "constant mean curvature surfaces",
      "nondegeneracy",
      "cmc surfaces",
      "conjugate cousin construction",
      "explicit upper bound"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......7153K"
    }
  }
}