{
  "abstract": "For the $\\mathrm{PGL}_3$-Hitchin moduli space of unmarked convex $\\mathbb{RP}^2$ structures on the surface $S_{g,m}$ with fixed boundary data $\\mathbf L$ when $m>0$, we investigate the subset whose canonical Hilbert--Busemann area is bounded above by $t$. We show that the Goldman symplectic volume of this subset is at most $C_{g,m}(t+λ^2)^{8g-8+3m}$, where $λ$ is the largest total-root boundary length for $m>0$ and is set to $0$ for $m=0$. As a consequence, We obtain the explicit upper bound for the $e^{-s\\cdot\\mathrm{Area}}$-weighted volume.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33417",
  "author_total": 4,
  "authors": [
    {
      "name": "Qiongling Li"
    },
    {
      "name": "Beibei Liu"
    },
    {
      "name": "Weixu Su"
    },
    {
      "name": "Zhe Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4vwah9fr492e8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33417",
  "fulltext_url": null,
  "id": "4vwah9fr492e8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33417",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7224003905",
  "pdf_url": "https://arxiv.org/pdf/2610.33417",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4vwah9fr492e8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.33417",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33417"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Volume of area-bounded PGL3-Hitchin moduli space",
  "title_text": "Volume of area-bounded PGL3-Hitchin moduli space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/4vwah9fr492e8",
  "venue": "arXiv",
  "versions": []
}