{
  "id": "1806.08816",
  "version": "v1",
  "published": "2018-06-22T18:41:26.000Z",
  "updated": "2018-06-22T18:41:26.000Z",
  "title": "Existence of infinitely many minimal hypersurfaces in closed manifolds",
  "authors": [
    "Antoine Song"
  ],
  "comment": "34 pages",
  "categories": [
    "math.DG",
    "math.AP",
    "math.GT"
  ],
  "abstract": "Using min-max theory, we show that in any closed Riemannian manifold of dimension at least 3 and at most 7, there exist infinitely many smoothly embedded closed minimal hypersurfaces. It proves a conjecture of S.-T. Yau. This paper builds on the methods developed by F. C. Marques and A. Neves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-22T18:41:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "closed manifolds",
      "smoothly embedded closed minimal hypersurfaces",
      "closed riemannian manifold",
      "min-max theory",
      "paper builds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}