{
  "id": "1004.5067",
  "version": "v1",
  "published": "2010-04-28T15:56:24.000Z",
  "updated": "2010-04-28T15:56:24.000Z",
  "title": "The visible part of plane self-similar sets",
  "authors": [
    "Kenneth J. Falconer",
    "Jonathan M. Fraser"
  ],
  "journal": "Proc. Amer. Math. Soc., 141, (2013), 269-278",
  "categories": [
    "math.MG"
  ],
  "abstract": "Given a compact subset $F$ of $\\mathbb{R}^2$, the visible part $V_\\theta F$ of $F$ from direction $\\theta$ is the set of $x$ in $F$ such that the half-line from $x$ in direction $\\theta$ intersects $F$ only at $x$. It is suggested that if $\\dim_H F \\geq 1$ then $\\dim_H V_\\theta F = 1$ for almost all $\\theta$, where $\\dim_H$ denotes Hausdorff dimension. We confirm this when $F$ is a self-similar set satisfying the convex open set condition and such that the orthogonal projection of $F$ onto every line is an interval. In particular the underlying similarities may involve arbitrary rotations and $F$ need not be connected.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-28T15:56:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80"
    ],
    "keywords": [
      "plane self-similar sets",
      "visible part",
      "convex open set condition",
      "denotes hausdorff dimension",
      "compact subset"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.5067F"
    }
  }
}