{
  "id": "2010.04991",
  "version": "v1",
  "published": "2020-10-10T13:25:13.000Z",
  "updated": "2020-10-10T13:25:13.000Z",
  "title": "Entropy rigidity for foliations by strictly convex projective manifolds",
  "authors": [
    "Alessio Savini"
  ],
  "comment": "11 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $N$ be a compact manifold with a foliation $\\mathscr{F}_N$ whose leaves are compact strictly convex projective manifolds. Let $M$ be a compact manifold with a foliation $\\mathscr{F}_M$ whose leaves are compact hyperbolic manifolds of dimension bigger than or equal to $3$. Suppose to have a foliation-preserving homeomorphism $f:(N,\\mathscr{F}_N) \\rightarrow (M,\\mathscr{F}_M)$ which is $C^1$-regular when restricted to leaves. In the previous situation there exists a well-defined notion of foliated volume entropies $h(N,\\mathscr{F}_N)$ and $h(M,\\mathscr{F}_M)$ and it holds $h(M,\\mathscr{F}_M) \\leq h(N,\\mathscr{F}_N)$. Additionally, if equality holds, then the leaves must be homothetic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-10T13:25:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C24",
      "57M50",
      "53A20"
    ],
    "keywords": [
      "entropy rigidity",
      "compact manifold",
      "compact strictly convex projective manifolds",
      "compact hyperbolic manifolds",
      "dimension bigger"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}