{
  "id": "2001.02707",
  "version": "v1",
  "published": "2020-01-08T19:18:43.000Z",
  "updated": "2020-01-08T19:18:43.000Z",
  "title": "Oriented Area as a Morse Function on Configuration Spaces of Necklaces",
  "authors": [
    "Daniil Mamaev"
  ],
  "comment": "12 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "Assume one has a necklace, that is, a closed string with a number of beads on it. Some of the beads are fixed, some can slide along the string. For a planar configuration of a necklace, the oriented area is well-defined. We characterise critical points of the oriented area function in geometric terms and give a formula for the Morse indices. Thus we obtain a generalisation of Jacob Steiner's isoperimetric theorems for polygons in the plane.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-08T19:18:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58K05",
      "52B60"
    ],
    "keywords": [
      "morse function",
      "configuration spaces",
      "jacob steiners isoperimetric theorems",
      "planar configuration",
      "characterise critical points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}