{
  "id": "1107.4803",
  "version": "v2",
  "published": "2011-07-24T21:49:25.000Z",
  "updated": "2014-01-22T00:08:19.000Z",
  "title": "Mean curvature flow of Lagrangian submanifolds with isolated conical singularities",
  "authors": [
    "Tapio Behrndt"
  ],
  "comment": "40 pages, 1 figure",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this paper we study the short time existence problem for the (generalized) Lagrangian mean curvature flow in (almost) Calabi--Yau manifolds when the initial Lagrangian submanifold has isolated conical singularities modelled on stable special Lagrangian cones. Given a Lagrangian submanifold $F_0:L\\rightarrow M$ in an almost Calabi--Yau manifold $M$ with isolated conical singularities at $x_1,...,x_n\\in M$ modelled on stable special Lagrangian cones $C_1,...,C_n$ in $\\mathbb{C}^m$, we show that for a short time there exist one-parameter families of points $x_1(t),... x_n(t)\\in M$ and a one parameter family of Lagrangian submanifolds $F(t,\\cdot):L\\rightarrow M$ with isolated conical singularities at $x_1(t),...,x_n(t)\\in M$ modelled on $C_1,...,C_n$, which evolves by (generalized) Lagrangian mean curvature flow with initial condition $F_0:L\\rightarrow M$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-01-22T00:08:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44",
      "35K55"
    ],
    "keywords": [
      "isolated conical singularities",
      "lagrangian submanifold",
      "lagrangian mean curvature flow",
      "stable special lagrangian cones",
      "short time existence problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.4803B"
    }
  }
}