{
  "id": "1707.08012",
  "version": "v1",
  "published": "2017-07-25T14:23:46.000Z",
  "updated": "2017-07-25T14:23:46.000Z",
  "title": "Min-max theory for constant mean curvature hypersurfaces",
  "authors": [
    "Xin Zhou",
    "Jonathan J. Zhu"
  ],
  "comment": "31 pages. Comments welcome!",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we develop a min-max theory for the construction of constant mean curvature (CMC) hypersurfaces of prescribed mean curvature in an arbitrary closed manifold. As a corollary, we prove the existence of a nontrivial, smooth, closed, almost embedded, CMC hypersurface of any given mean curvature $c$. Moreover, if $c$ is nonzero then our min-max solution always has multiplicity one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-25T14:23:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A10",
      "49J35",
      "53C42"
    ],
    "keywords": [
      "constant mean curvature hypersurfaces",
      "min-max theory",
      "prescribed mean curvature",
      "arbitrary closed manifold",
      "cmc hypersurface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}