{
  "id": "1009.1083",
  "version": "v3",
  "published": "2010-09-06T16:16:08.000Z",
  "updated": "2012-05-07T23:09:55.000Z",
  "title": "Finite Time Singularities for Lagrangian Mean Curvature Flow",
  "authors": [
    "André Neves"
  ],
  "comment": "Final version, to appear in Annals of Mathematics. Exposition improved. 46 pages",
  "categories": [
    "math.DG",
    "math.AP",
    "math.SG"
  ],
  "abstract": "Given any embedded Lagrangian on a four dimensional compact Calabi-Yau, we find another Lagrangian in the same Hamiltonian isotopy class which develops a finite time singularity under mean curvature flow. This contradicts a weaker version of the Thomas-Yau conjecture regarding long time existence and convergence of Lagrangian mean curvature flow.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-05-07T23:09:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lagrangian mean curvature flow",
      "finite time singularity",
      "thomas-yau conjecture regarding long time",
      "conjecture regarding long time existence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.1083N"
    }
  }
}