{
  "id": "2210.02295",
  "version": "v1",
  "published": "2022-10-05T14:33:19.000Z",
  "updated": "2022-10-05T14:33:19.000Z",
  "title": "Smooth rigidity for 3-dimensional volume preserving Anosov flows and weighted marked length spectrum rigidity",
  "authors": [
    "Andrey Gogolev",
    "Federico Rodriguez Hertz"
  ],
  "comment": "19 pages, 1 figure",
  "categories": [
    "math.DS",
    "math.DG"
  ],
  "abstract": "Let $X_1^t$ and $X_2^t$ be volume preserving Anosov flows on a 3-dimensional manifold $M$. We prove that if $X_1^t$ and $X_2^t$ are $C^0$ conjugate then the conjugacy is, in fact, smooth, unless $M$ is a mapping torus of an Anosov automorphism of $\\mathbb T^2$ and both flows are constant roof suspension flows. We deduce several applications. Among them is a new result on rigidity of Anosov diffeorphisms on $\\mathbb T^2$ and a new \"weighted\" marked length spectrum rigidity result for surfaces of negative curvature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-05T14:33:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "volume preserving anosov flows",
      "weighted marked length spectrum rigidity",
      "smooth rigidity",
      "length spectrum rigidity result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}