{
  "id": "math/0603615",
  "version": "v2",
  "published": "2006-03-27T11:40:17.000Z",
  "updated": "2008-05-30T10:47:15.000Z",
  "title": "Unstable minimal surfaces of annulus type in manifolds",
  "authors": [
    "Hwajeong Kim"
  ],
  "comment": "36pages",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "Unstable minimal surfaces are the unstable stationary points of the Dirichlet-Integral. In order to obtain unstable solutions, the method of the gradient flow together with the minimax-principle is generally used. The application of this method for minimal surfaces in the Euclidean spacce was presented in \\cite{s3}. We extend this theory for obtaining unstable minimal surfaces in Riemannian manifolds. In particular, we handle minimal surfaces of annulus type, i.e. we prescribe two Jordan curves of class $C^3$ in a Riemannian manifold and prove the existence of unstable minimal surfaces of annulus type bounded by these curves.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-05-30T10:47:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q05",
      "58E05"
    ],
    "keywords": [
      "annulus type",
      "riemannian manifold",
      "handle minimal surfaces",
      "euclidean spacce",
      "obtaining unstable minimal surfaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3615K"
    }
  }
}