{
  "id": "2206.02105",
  "version": "v1",
  "published": "2022-06-05T06:38:45.000Z",
  "updated": "2022-06-05T06:38:45.000Z",
  "title": "Estimating the Morse index of free boundary minimal hypersurfaces through covering arguments",
  "authors": [
    "Santiago Cordero-Misteli",
    "Giada Franz"
  ],
  "comment": "21 pages, 3 figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "Given a compact Riemannian manifold with boundary of dimension between 3 and 7, we show that the Morse index of a free boundary minimal hypersurface grows linearly with the sum of its Betti numbers, where the constant of growth depends on the area of the free boundary minimal hypersurface in question. We are inspired by a groundbreaking combinatorial argument by Song (2019), which we partly simplify and shorten.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-05T06:38:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "morse index",
      "covering arguments",
      "free boundary minimal hypersurface grows",
      "compact riemannian manifold",
      "estimating"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}