{
  "id": "1901.03316",
  "version": "v1",
  "published": "2019-01-10T18:37:14.000Z",
  "updated": "2019-01-10T18:37:14.000Z",
  "title": "Compactification of the space of Hamiltonian stationary Lagrangian submanifolds with bounded total extrinsic curvature and volume",
  "authors": [
    "Jingyi Chen",
    "Micah Warren"
  ],
  "comment": "27 pages",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "For a sequence of immersed connected closed Hamiltonian stationary Lagrangian submaniolds in $\\mathbb{C}^{n}$ with uniform bounds on their volumes and the total extrinsic curvatures, we prove that a subsequence converges either to a point or to a Hamiltonian stationary Lagrangian $n$-varifold locally uniformly in $C^{k}$ for any nonnegative integer $k$ away from a finite set of points, and the limit is Hamiltonian stationary in ${\\mathbb{C}}^{n}$. We also obtain a theorem on extending Hamiltonian stationary Lagrangian submanifolds $L$ across a compact set $N$ of Hausdorff codimension at least 2 that is locally noncollapsing in volumes matching its Hausdorff dimension, provided the mean curvature of $L$ is in $L^{n}$ and a condition on local volume of $L$ near $N$ is satisfied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-10T18:37:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C42",
      "35J30",
      "35J60"
    ],
    "keywords": [
      "hamiltonian stationary lagrangian submanifolds",
      "bounded total extrinsic curvature",
      "hamiltonian stationary lagrangian submaniolds",
      "closed hamiltonian stationary lagrangian",
      "connected closed hamiltonian stationary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}