{
  "id": "2008.13728",
  "version": "v1",
  "published": "2020-08-31T16:45:15.000Z",
  "updated": "2020-08-31T16:45:15.000Z",
  "title": "Dynamical instability of minimal surfaces at flat singular points",
  "authors": [
    "Salvatore Stuvard",
    "Yoshihiro Tonegawa"
  ],
  "comment": "28 pages, 3 figures. Comments are welcome!",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "Suppose that a countably $n$-rectifiable set $\\Gamma_0$ is the support of a multiplicity-one stationary varifold in $\\mathbb{R}^{n+1}$ with a point admitting a flat tangent plane $T$ of density $Q \\geq 2$. We prove that, under a suitable assumption on the decay rate of the blow-ups of $\\Gamma_0$ towards $T$, there exists a non-constant Brakke flow starting with $\\Gamma_0$. This shows non-uniqueness of Brakke flow under these conditions, and suggests that the stability of a stationary varifold with respect to mean curvature flow may be used to exclude the presence of flat singularities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-31T16:45:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53E10",
      "49Q05"
    ],
    "keywords": [
      "flat singular points",
      "minimal surfaces",
      "dynamical instability",
      "mean curvature flow",
      "flat tangent plane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}