{
  "id": "1106.4910",
  "version": "v1",
  "published": "2011-06-24T08:52:55.000Z",
  "updated": "2011-06-24T08:52:55.000Z",
  "title": "On Projections of Metric Spaces",
  "authors": [
    "Mark Kozdoba"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $X$ be a metric space and let $\\mu$ be a probability measure on it. Consider a Lipschitz map $T: X \\rightarrow \\Rn$, with Lipschitz constant $\\leq 1$. Then one can ask whether the image $TX$ can have large projections on many directions. For a large class of spaces $X$, we show that there are directions $\\phi \\in \\nsphere$ on which the projection of the image $TX$ is small on the average, with bounds depending on the dimension $n$ and the eigenvalues of the Laplacian on $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-24T08:52:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "metric space",
      "probability measure",
      "large class",
      "lipschitz map",
      "directions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.4910K"
    }
  }
}