{
  "id": "2407.02755",
  "version": "v1",
  "published": "2024-07-03T02:14:49.000Z",
  "updated": "2024-07-03T02:14:49.000Z",
  "title": "A generalization of a Theorem of A. Rogers",
  "authors": [
    "Efren Morales-Amaya"
  ],
  "categories": [
    "math.MG"
  ],
  "abstract": "Generalizing a Theorem due to A. Rogers \\cite{ro1}, we are going to prove that if for a pair of convex bodies $K_{1},K_{2}\\subset \\Rn$, $n\\geq 3$, there exists a hyperplane $H$ and a pair of different points $p_1$ and $p_2$ in $\\Rn \\backslash H$ such that for each $(n-2)$-plane $M\\subset H$, there exists a \\textit{mirror} which maps the hypersection of $K_1$ defined by $\\aff\\{ p_1,M\\}$ onto the hypersection of $K_2$ defined by $\\aff\\{ p_2,M\\}$, then there exists a \\textit{mirror} which maps $K_1$ onto $K_2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-03T02:14:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalization",
      "convex bodies",
      "hypersection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}