{
  "id": "2406.13428",
  "version": "v1",
  "published": "2024-06-19T10:39:01.000Z",
  "updated": "2024-06-19T10:39:01.000Z",
  "title": "Petty projection inequality on the sphere and on the hyperbolic space",
  "authors": [
    "Y. Lin",
    "Y. Wu"
  ],
  "categories": [
    "math.MG"
  ],
  "abstract": "Using gnomonic projection and Poincar\\'e model, we first define the spherical projection body and hyperbolic projection body in spherical space $\\mathbb{S}^n$ and hyperbolic space $\\mathbb{H}^n$, then define the spherical Steiner symmetrization and hyperbolic Steiner symmetrization, finally prove the spherical projection inequality and hyperbolic projection inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-19T10:39:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A55",
      "28A75",
      "52A20",
      "53A35"
    ],
    "keywords": [
      "petty projection inequality",
      "hyperbolic space",
      "hyperbolic steiner symmetrization",
      "hyperbolic projection inequality",
      "hyperbolic projection body"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}