{
  "annotation_id": "377f4485-1ec8-43da-946b-f7ab68f8d912",
  "date_created": "2026-02-17T05:53:05.056000Z",
  "date_modified": "2026-02-17T05:53:05.056000Z",
  "file_hash": "0ad7ffff3e4603f378c5b601a0705c9e49b52e022f76cb0b6ed0f38ef61f2f7e",
  "private": false,
  "record": {
    "abstract": "A theorem of Meyer and Reisner characterizes ellipsoids by the collinearity of centroids of parallel sections: if $\\Omega\\subset\\mathbb{R}^{n+1}$ is a convex body such that for every $n$-dimensional subspace $M\\subset\\mathbb{R}^{n+1}$ the centroids of the sections $(x+M)\\cap \\Omega$ are collinear, then $\\Omega$ is an ellipsoid.\n  We study natural extensions of this centroid-collinearity condition to unbounded convex sets. In particular, we show that among affine hyperspheres, precisely the ellipsoids, paraboloids and one sheet of a two-sheeted hyperboloid satisfy this property. We also identify additional assumptions under which any convex hypersurface with this property must necessarily be a quadric.",
    "arxiv_id": "2601.06107",
    "authors": [
      "Alexandre Borentain"
    ],
    "categories": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "A Characterization of Quadrics Among Affine Hyperspheres by Section-Centroid Location",
    "url": "https://arxiv.org/abs/2601.06107",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9d94a83f-7a01-450b-a375-303a03fdbdb7",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}