{
  "id": "2204.11968",
  "version": "v1",
  "published": "2022-04-25T21:15:02.000Z",
  "updated": "2022-04-25T21:15:02.000Z",
  "title": "Some remarks on critical sets of Laplace eigenfunctions",
  "authors": [
    "Chris Judge",
    "Sugata Mondal"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "We study the set of critical points of a solution to $\\Delta u = \\lambda \\cdot u$ and in particular components of the critical set that have codimension 1. We show, for example, that if a second Neumann eigenfunction of a simply connected polygon $P$ has infinitely many critical points, then $P$ is a rectangle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-25T21:15:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J05"
    ],
    "keywords": [
      "critical set",
      "laplace eigenfunctions",
      "critical points",
      "second neumann eigenfunction",
      "components"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}