{
  "id": "2202.07151",
  "version": "v1",
  "published": "2022-02-15T02:55:52.000Z",
  "updated": "2022-02-15T02:55:52.000Z",
  "title": "A compactness theorem for hyperkaehler 4-manifolds with boundary",
  "authors": [
    "Hongyi Liu"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we study the compactness of a boundary value problem for hyperkaehler 4-manifolds. We show that under certain topological conditions and the positive mean curvature condition on the boundary, a sequence of hyperkaehler triples converges smoothly up to diffeomorphisms if and only if their restrictions to the boundary converge smoothly up to diffeomorphisms. We also generalize this result to torsion-free hypersymplectic triples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-15T02:55:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compactness theorem",
      "torsion-free hypersymplectic triples",
      "hyperkaehler triples converges",
      "boundary value problem",
      "positive mean curvature condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}