{
  "id": "1709.05020",
  "version": "v1",
  "published": "2017-09-15T00:55:06.000Z",
  "updated": "2017-09-15T00:55:06.000Z",
  "title": "On the Existence of a Closed, Embedded, Rotational $λ$-Hypersurface",
  "authors": [
    "John Ross"
  ],
  "comment": "11 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper we show the existence of a closed, embedded $\\lambda$-hypersurfaces $\\Sigma \\subset \\mathbb{R}^{2n}$. The hypersurface is diffeomorhic to $\\mathbb{S}^{n-1} \\times \\mathbb{S}^{n-1} \\times \\mathbb{S}^1$ and exhibits $SO(n) \\times SO(n)$ symmetry. Our approach uses a \"shooting method\" similar to the approach used by McGrath in constructing a generalized self-shrinking torus solution to mean curvature flow. The result generalizes the $\\lambda$-torus found by Cheng and Wei.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-15T00:55:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A10"
    ],
    "keywords": [
      "hypersurface",
      "rotational",
      "mean curvature flow",
      "result generalizes",
      "generalized self-shrinking torus solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}