{
  "id": "0904.1255",
  "version": "v2",
  "published": "2009-04-08T02:38:37.000Z",
  "updated": "2009-09-24T20:43:15.000Z",
  "title": "Examples of hypersurfaces flowing by curvature in a Riemannian manifold",
  "authors": [
    "Robert Gulliver",
    "Guoyi Xu"
  ],
  "comment": "some changes, 18 pages, no figures, accepted by Comm. Anal. Geom",
  "journal": "Comm. Anal. Geom. 17 (2009), no. 4, 701-719",
  "categories": [
    "math.DG"
  ],
  "abstract": "This paper gives some examples of hypersurfaces $\\phi_t(M^n)$ evolving in time with speed determined by functions of the normal curvatures in an $(n+1)$-dimensional hyperbolic manifold; we emphasize the case of flow by harmonic mean curvature. The examples converge to a totally geodesic submanifold of any dimension from 1 to $n$, and include cases which exist for infinite time. Convergence to a point was studied by Andrews, and only occurs in finite time. For dimension $n=2,$ the destiny of any harmonic mean curvature flow is strongly influenced by the genus of the surface $M^2$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-09-24T20:43:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K15",
      "53C44"
    ],
    "keywords": [
      "riemannian manifold",
      "hypersurfaces flowing",
      "harmonic mean curvature flow",
      "dimensional hyperbolic manifold",
      "examples converge"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.1255G"
    }
  }
}