{
  "id": "1909.02535",
  "version": "v1",
  "published": "2019-09-05T17:17:58.000Z",
  "updated": "2019-09-05T17:17:58.000Z",
  "title": "Codimension Bounds and Rigidity of Ancient Mean Curvature Flows by the Tangent Flow at $-\\infty$",
  "authors": [
    "Douglas Stryker",
    "Ao Sun"
  ],
  "comment": "20 pages, comments are welcomed!",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "Motivated by the limiting behavior of an explicit class of compact ancient curve shortening flows, we prove codimension bounds for ancient mean curvature flows by their tangent flow at $-\\infty$, generalizing a theorem for cylinders in [CM19b]. In the case of the $m$-covered circle, we apply this bound to prove a strong rigidity theorem. Furthermore, we extend this paradigm by showing that under the assumption of sufficiently rapid convergence, a compact ancient mean curvature flow is identical to its tangent flow at $-\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-05T17:17:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44"
    ],
    "keywords": [
      "tangent flow",
      "codimension bounds",
      "compact ancient mean curvature flow",
      "compact ancient curve shortening flows"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}