{
"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"
}
}
}