{
  "abstract": "We show that for $k>1$ the number of genus $k$ minimal Lagrangians with area at most $A$ in a product of hyperbolic surfaces grows on the order of $A^{6(k-1)}$, with an explicit leading constant given in terms of the Mirzakhani function, and we obtain a similar result for products of nonpositively curved surfaces. We also prove rigidity of the Lagrangian area spectrum, and obtain analogous counting results for products of a higher genus surface with a circle.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.04614",
  "author_total": 3,
  "authors": [
    {
      "name": "Ben Lowe"
    },
    {
      "name": "Fernando C. Marques"
    },
    {
      "name": "André Neves"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4bxd5ec2fz8jg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.04614",
  "fulltext_url": null,
  "id": "4bxd5ec2fz8jg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.04614",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7160548183",
  "pdf_url": "https://arxiv.org/pdf/2605.04614",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4bxd5ec2fz8jg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2605.04614",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.04614"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Counting Minimal Lagrangians Via Mirzakhani Functions",
  "title_text": "Counting Minimal Lagrangians Via Mirzakhani Functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/4bxd5ec2fz8jg",
  "venue": "arXiv",
  "versions": []
}