{
  "id": "2309.06974",
  "version": "v1",
  "published": "2023-09-13T14:06:27.000Z",
  "updated": "2023-09-13T14:06:27.000Z",
  "title": "Planar loops with prescribed curvature via Hardy's inequality",
  "authors": [
    "Gabriele Cora",
    "Roberta Musina"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "We investigate the existence of closed planar loops with prescribed curvature. Our approach is variational, and relies on a Hardy type inequality and its associated functional space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-13T14:06:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A04",
      "51M25",
      "35J50",
      "53C42"
    ],
    "keywords": [
      "prescribed curvature",
      "hardys inequality",
      "hardy type inequality",
      "closed planar loops",
      "associated functional space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}