{
  "id": "1502.02299",
  "version": "v1",
  "published": "2015-02-08T20:28:16.000Z",
  "updated": "2015-02-08T20:28:16.000Z",
  "title": "Endpoint regularity of $2$d Mumford-Shah minimizers",
  "authors": [
    "Camillo De Lellis",
    "Matteo Focardi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove an $\\varepsilon$-regularity theorem at the endpoint of connected arcs for $2$-dimensional Mumford-Shah minimizers. In particular we show that, if in a given ball $B_r (x)$ the jump set of a given Mumford-Shah minimizer is sufficiently close, in the Hausdorff distance, to a radius of $B_r (x)$, then in a smaller ball the jump set is a connected arc which terminates at some interior point $y_0$ and it is $C^{1,\\alpha}$ up to $y_0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-08T20:28:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "endpoint regularity",
      "jump set",
      "dimensional mumford-shah minimizers",
      "connected arc",
      "regularity theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150202299D"
    }
  }
}