{
  "id": "math/0608401",
  "version": "v1",
  "published": "2006-08-15T19:11:02.000Z",
  "updated": "2006-08-15T19:11:02.000Z",
  "title": "Singularities of Lagrangian mean curvature flow: monotone case",
  "authors": [
    "Andre' Neves"
  ],
  "comment": "18 pages. 2 figures. Submitted",
  "categories": [
    "math.DG",
    "math.SG"
  ],
  "abstract": "We study the formation of singularities for the mean curvature flow of monotone Lagrangians in $\\C^n$. More precisely, we show that if singularities happen before a critical time then the tangent flow can be decomposed into a finite union of area-minimizing Lagrangian cones (Slag cones). When $n=2$, we can improve this result by showing that connected components of the rescaled flow converge to an area-minimizing cone, as opposed to possible non-area minimizing union of Slag cones. In the last section, we give specific examples for which such singularity formation occurs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-08-15T19:11:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44"
    ],
    "keywords": [
      "lagrangian mean curvature flow",
      "monotone case",
      "slag cones",
      "singularity formation occurs",
      "area-minimizing lagrangian cones"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8401N"
    }
  }
}