{
  "id": "1805.12540",
  "version": "v1",
  "published": "2018-05-29T16:11:01.000Z",
  "updated": "2018-05-29T16:11:01.000Z",
  "title": "Evolution of Contractions between Non-Compact Manifolds",
  "authors": [
    "Felix Lubbe"
  ],
  "comment": "29 pages; comments are welcome! arXiv admin note: text overlap with arXiv:1608.05394, and with arXiv:1602.07595 by other authors",
  "categories": [
    "math.DG"
  ],
  "abstract": "Let $N$ be a complete manifold with bounded geometry, such that $\\sec_N\\le -\\sigma < 0$ for some positive constant $\\sigma$. We investigate the mean curvature flow of the graphs of smooth length-decreasing maps $f:\\mathbb{R}^m\\to N$. In this case, the solution exists for all times and the evolving submanifold stays the graph of a length-decreasing map $f_t$. We further prove uniform decay estimates for all derivatives of order $\\ge 2$ of $f_t$ along the flow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-29T16:11:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44",
      "53C42",
      "53C21"
    ],
    "keywords": [
      "non-compact manifolds",
      "contractions",
      "mean curvature flow",
      "uniform decay estimates",
      "evolving submanifold stays"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}