{
  "id": "1512.03886",
  "version": "v1",
  "published": "2015-12-12T07:18:02.000Z",
  "updated": "2015-12-12T07:18:02.000Z",
  "title": "Gradient estimates for mean curvature flow with Neumann boundary conditions",
  "authors": [
    "Masashi Mizuno",
    "Keisuke Takasao"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the mean curvature flow of graphs both with Neumann boundary conditions and transport terms. We derive boundary gradient estimates for the mean curvature flow. As an application, the existence of the mean curvature flow of graphs is presented. A key argument is a boundary monotonicity formula of a Huisken type derived using reflected backward heat kernels. Furthermore, we provide regularity conditions for the transport terms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-12T07:18:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K93",
      "53C44",
      "35B65"
    ],
    "keywords": [
      "mean curvature flow",
      "neumann boundary conditions",
      "transport terms",
      "derive boundary gradient estimates",
      "boundary monotonicity formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}