{
  "id": "2212.12748",
  "version": "v1",
  "published": "2022-12-24T15:12:21.000Z",
  "updated": "2022-12-24T15:12:21.000Z",
  "title": "Non-degeneracy of critical points of the squared norm of the second fundamental form on manifolds with minimal boundary",
  "authors": [
    "Sergio Cruz-Blázquez",
    "Angela Pistoia"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "Let $(M,\\bar g)$ be a compact Riemannian manifold with minimal boundary such that the second fundamental form is nowhere vanishing on $\\partial M$. We show that for a generic Riemannian metric $\\bar g$, the squared norm of the second fundamental form is a Morse function, i.e. all its critical points are non-degenerate. We show that the generality of this property holds when we restrict ourselves to the conformal class of the initial metric on $M$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-24T15:12:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J60",
      "53C21"
    ],
    "keywords": [
      "second fundamental form",
      "minimal boundary",
      "critical points",
      "squared norm",
      "non-degeneracy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}