{
  "id": "1907.11520",
  "version": "v1",
  "published": "2019-07-26T12:36:36.000Z",
  "updated": "2019-07-26T12:36:36.000Z",
  "title": "Propagation of a Mean Curvature Flow in a Cone",
  "authors": [
    "Bendong Lou"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We consider a mean curvature flow in a cone, that is, a hypersurface in a cone which moves toward the opening with normal velocity equaling to the mean curvature, and the contact angle between the hypersurface and the cone boundary being $\\varepsilon$-periodic in its position. First, by constructing a family of self-similar solutions, we give a priori estimates for the radially symmetric solutions and prove the global existence. Then we consider the homogenization limit as $\\ve\\to 0$, and use {\\it the slowest self-similar solution} to characterize the solution, with error $O(1)\\ve^{1/6}$, in some finite time interval.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-26T12:36:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K93",
      "35R35",
      "35C06",
      "35B27"
    ],
    "keywords": [
      "mean curvature flow",
      "propagation",
      "finite time interval",
      "slowest self-similar solution",
      "hypersurface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}