{
  "id": "0709.2977",
  "version": "v1",
  "published": "2007-09-19T09:41:57.000Z",
  "updated": "2007-09-19T09:41:57.000Z",
  "title": "Minimal surfaces in sub-Riemannian manifolds and structure of their singular sets in the (2,3) case",
  "authors": [
    "Nataliya Shcherbakova"
  ],
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "We study minimal surfaces in generic sub-Riemannian manifolds with sub-Riemannian structures of co-rank one. These surfaces can be defined as the critical points of the so-called {\\it horizontal} area functional associated to the canonical {\\it horizontal} area form. We derive the intrinsic equation in the general case and then consider in greater detail 2-dimensional surfaces in contact manifolds of dimension 3. We show that in this case minimal surfaces are projections of a special class of 2-dimensional surfaces in the horizontal spherical bundle over the base manifold. Generic singularities of minimal surfaces turn out the singularities of this projection, and we give a complete local classification of them. We illustrate our results by examples in the Heisenberg group and the group of roto-translations",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-09-19T09:41:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C17",
      "32S25"
    ],
    "keywords": [
      "singular sets",
      "complete local classification",
      "generic sub-riemannian manifolds",
      "case minimal surfaces",
      "horizontal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.2977S"
    }
  }
}