{
  "id": "0906.2981",
  "version": "v1",
  "published": "2009-06-16T17:13:27.000Z",
  "updated": "2009-06-16T17:13:27.000Z",
  "title": "Mean curvature flow of graphs in warped products",
  "authors": [
    "Alexander A. Borisenko",
    "Vicente Miquel"
  ],
  "comment": "39 pages, 2 figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "Let $M$ be a complete Riemannian manifold which either is compact or has a pole, and let $\\varphi$ be a positive smooth function on $M$. In the warped product $M\\times_\\varphi\\mathbb R$, we study the flow by the mean curvature of a locally Lipschitz continuous graph on $M$ and prove that the flow exists for all time and that the evolving hypersurface is $C^\\infty$ for $t>0$ and is a graph for all $t$. Moreover, under certain conditions, the flow has a well defined limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-06-16T17:13:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44"
    ],
    "keywords": [
      "mean curvature flow",
      "warped product",
      "complete riemannian manifold",
      "positive smooth function",
      "locally lipschitz continuous graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.2981B"
    }
  }
}