{
  "id": "1607.02899",
  "version": "v1",
  "published": "2016-07-11T10:57:22.000Z",
  "updated": "2016-07-11T10:57:22.000Z",
  "title": "Collapse of the mean curvature flow for certain kind of invariant hypersurfaces in a Hilbert space",
  "authors": [
    "Naoyuki Koike"
  ],
  "comment": "47pages. arXiv admin note: text overlap with arXiv:1210.2539",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we investigate the regularized mean curvature flow starting from an invariant hypersurface in a Hilbert space equipped with an isometric and almost free action of a Hilbert Lie group whose orbits are regularized minimal. We prove that, if the invariant hypersurface satisfies a certain kind of horizontally convexity condition, then it collapses to an orbit of the Hilbert Lie group action along the regularized mean curvature flow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-11T10:57:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hilbert space",
      "regularized mean curvature flow",
      "mean curvature flow starting",
      "hilbert lie group action",
      "invariant hypersurface satisfies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}