{
  "id": "1411.5405",
  "version": "v1",
  "published": "2014-11-19T23:49:52.000Z",
  "updated": "2014-11-19T23:49:52.000Z",
  "title": "Eigenvalues and Entropy of a Hitchin representation",
  "authors": [
    "Rafael Potrie",
    "Andrés Sambarino"
  ],
  "comment": "29 pages, 4 figures",
  "categories": [
    "math.GR",
    "math.DG"
  ],
  "abstract": "We show that the critical exponent of a representation in the Hitchin component of $PSL(d,\\mathbb{R})$ is bounded above, the least upper bound being attained only in the Fuchsian locus. This provides a rigid inequality for the area of a minimal surface on $\\rho\\backslash X,$ where $X$ is the symmetric space of $PSL(d,\\mathbb{R}).$ The proof relies in a construction useful to prove a regularity statement: if $\\rho$ belongs to the Hitchin component of $Psp(2k,\\mathbb{R}),$ $PSO(k,k+1)$ or $G_2,$ and its Frenet curve is smooth then $\\rho$ is Fuchsian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-19T23:49:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hitchin representation",
      "eigenvalues",
      "hitchin component",
      "upper bound",
      "frenet curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.5405P"
    }
  }
}