{
  "id": "1906.07609",
  "version": "v1",
  "published": "2019-06-18T14:30:58.000Z",
  "updated": "2019-06-18T14:30:58.000Z",
  "title": "Entropy and codimension bounds for generic singularities",
  "authors": [
    "Tobias Holck Colding",
    "William P. Minicozzi II"
  ],
  "categories": [
    "math.DG",
    "math.AP",
    "math.GT",
    "math.SP"
  ],
  "abstract": "We show that all closed $2$-dimensional singularities for higher codimension mean curvature flow that cannot be perturbed away have uniform entropy bounds and lie in a linear subspace of small dimension. The entropy and dimension of the subspace are both $\\leq C\\,(1+\\gamma)$ for some universal constant $C$ and genus $\\gamma$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-18T14:30:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generic singularities",
      "codimension bounds",
      "higher codimension mean curvature flow",
      "uniform entropy bounds",
      "universal constant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}