{
  "id": "2306.12258",
  "version": "v1",
  "published": "2023-06-21T13:27:58.000Z",
  "updated": "2023-06-21T13:27:58.000Z",
  "title": "Rigidity of contracting map using harmonic map heat flow",
  "authors": [
    "Man-Chun Lee",
    "Jingbo Wan"
  ],
  "comment": "10 pages, all comments are wellcome",
  "categories": [
    "math.DG",
    "math.AP",
    "math.GT"
  ],
  "abstract": "Motivated by the recent work of Tsai-Tsui-Wang, we consider the rigidity of map between compact manifolds with positive curvature. We show that distance non-increasing map between complex projective spaces is either an isometry or homotopically trivial. The rigidity result also holds on a wider class of manifolds with positive curvature and weaker contracting property on the map in between distance non-increasing and area non-increasing. This is based on the harmonic map heat flow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-21T13:27:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harmonic map heat flow",
      "contracting map",
      "positive curvature",
      "wider class",
      "rigidity result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}