{
  "id": "1512.08527",
  "version": "v1",
  "published": "2015-12-28T21:04:19.000Z",
  "updated": "2015-12-28T21:04:19.000Z",
  "title": "Compactness properties of Ricci flows with bounded scalar curvature",
  "authors": [
    "Richard H. Bamler"
  ],
  "comment": "151 pages",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this paper we prove a compactness result for Ricci flows with bounded scalar curvature and entropy. It states that given any sequence of such Ricci flows, we can pass to a subsequence that converges to a metric space which is smooth away from a set of codimension $\\geq 4$. The result has two main consequences: First, it implies that singularities in Ricci flows with bounded scalar curvature have codimension $\\geq 4$ and, second, it establishes a general form of the Hamilton-Tian Conjecture, which is even true in the Riemannian case. In the course of the proof, we will also establish the following results: $L^{p < 4}$ curvature bounds, integral bounds on the curvature radius, Gromov-Hausdorff closeness of time-slices, an $\\varepsilon$-regularity theorem for Ricci flows and an improved backwards pseudolocality theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-28T21:04:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded scalar curvature",
      "ricci flows",
      "compactness properties",
      "compactness result",
      "pseudolocality theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 151,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151208527B"
    }
  }
}