{
  "id": "2212.14456",
  "version": "v1",
  "published": "2022-12-29T20:54:01.000Z",
  "updated": "2022-12-29T20:54:01.000Z",
  "title": "How far apart can the projection of the centroid of a convex body and the centroid of its projection be?",
  "authors": [
    "Sergii Myroshnychenko",
    "Kateryna Tatarko",
    "Vladyslav Yaskin"
  ],
  "comment": "13 pages, 1 figure",
  "categories": [
    "math.MG",
    "math.FA"
  ],
  "abstract": "We show that there is a constant $D \\approx 0.2016$ such that for every $n$, every convex body $K\\subset \\mathbb R^n$, and every hyperplane $H\\subset \\mathbb R^n$, the distance between the projection of the centroid of $K$ onto $H$ and the centroid of the projection of $K$ onto $H$ is at most $D$ times the width of $K$ in the direction of the segment connecting the two points. The constant $D$ is asymptotically sharp.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-29T20:54:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A20",
      "52A40"
    ],
    "keywords": [
      "projection",
      "convex body",
      "far apart",
      "asymptotically sharp"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}