{
  "id": "2012.13067",
  "version": "v1",
  "published": "2020-12-24T02:04:09.000Z",
  "updated": "2020-12-24T02:04:09.000Z",
  "title": "Stability property and Dirichlet problem for translating solitons",
  "authors": [
    "Li Ma",
    "Vicente Miquel"
  ],
  "comment": "15 pages",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this paper, we prove that the infimum of the mean curvature is zero for a translating solitons of hypersurface in $\\re^{n+k}$. We give some conditions under which a complete hypersurface translating soliton is stable. We show that if the norm of its mean curvature is less than one, then the weighted volume may have exponent growth. We also study the Dirichlet problem for graphic translating solitons in higher codimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-24T02:04:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirichlet problem",
      "stability property",
      "mean curvature",
      "complete hypersurface translating soliton",
      "higher codimensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}