{
  "id": "math/0603735",
  "version": "v2",
  "published": "2006-03-31T09:19:37.000Z",
  "updated": "2008-09-02T14:17:27.000Z",
  "title": "Curves in Banach spaces which allow a $C^2$ parametrization",
  "authors": [
    "Jakub Duda",
    "Ludek Zajicek"
  ],
  "comment": "22 pages; We split the original paper into two parts. This is the first part ($C^2$ paths), the second part (paths with finite convexity) will appear later",
  "doi": "10.1112/jlms/jdq100",
  "categories": [
    "math.CA",
    "math.DG"
  ],
  "abstract": "We give a complete characterization of those $f: [0,1] \\to X$ (where $X$ is a Banach space which admits an equivalent Fr\\'echet smooth norm) which allow an equivalent $C^2$ parametrization. For $X=\\R$, a characterization is well-known. However, even in the case $X=\\R^2$, several quite new ideas are needed. Moreover, the very close case of parametrizations with a bounded second derivative is solved.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-09-02T14:17:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26E20",
      "26A51",
      "53A04"
    ],
    "keywords": [
      "banach space",
      "parametrization",
      "equivalent frechet smooth norm",
      "complete characterization",
      "close case"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3735D"
    }
  }
}