{
  "id": "2102.03508",
  "version": "v1",
  "published": "2021-02-06T04:29:09.000Z",
  "updated": "2021-02-06T04:29:09.000Z",
  "title": "On the noncollapsedness of positively curved Type I ancient Ricci flows",
  "authors": [
    "Liang Cheng",
    "Yongjia Zhang"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "In this article, we study complete Type I ancient Ricci flows with positive sectional curvature. Our main results are as follows: in the complete and noncompact case, all such ancient solutions must be noncollapsed on all scales; in the closed case, if the dimension is even, then all such ancient solutions must be noncollapsed on all scales. This furthermore gives a complete classification for three-dimensional noncompact Type I ancient solutions without assuming the noncollapsing condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-06T04:29:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ancient ricci flows",
      "positively curved type",
      "ancient solutions",
      "noncollapsedness",
      "study complete type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}