{
  "abstract": "We establish several results about Patterson--Sullivan measures for relatively Anosov groups. First, we prove that these measures are exact dimensional with respect to visual metrics induced by Gromov models in the Groves--Manning quasi-isometry class. Under the additional assumption that the group is relatively Morse, we show that the associated scalar Cartan metric is Gromov hyperbolic and that the corresponding boundary premetric is a visual metric to which the exact-dimensionality theorem applies. Second, we prove that their Manhattan manifolds are $C^1$-regular, from which we deduce that the growth indicator is $C^1$-regular and strictly concave on the interior of the limit cone. This extends the case of Anosov representations by Kim--Oh--Wang. Our methods are dynamical, and we exploit the fact due to Kim--Oh and Blayac--Canary--Zhu--Zimmer that Bowen--Margulis--Sullivan measures for relatively Anosov groups are finite and mixing.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.13730",
  "author_total": 2,
  "authors": [
    {
      "name": "Eduardo Reyes"
    },
    {
      "name": "Tianqi Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ecjjbkw4hnqvv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.13730",
  "fulltext_url": null,
  "id": "ecjjbkw4hnqvv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.13730",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.GT"
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      "openalex",
      "2610|Mathematical Dynamics and Fractals"
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  "openalex": "W7168966635",
  "pdf_url": "https://arxiv.org/pdf/2607.13730",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ecjjbkw4hnqvv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2607.13730",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.13730"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Regularity of Manhattan manifolds and exact dimensionality for relatively Anosov groups",
  "title_text": "Regularity of Manhattan manifolds and exact dimensionality for relatively Anosov groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/ecjjbkw4hnqvv",
  "venue": "arXiv",
  "versions": []
}