{
  "abstract": "Let $S$ be a closed oriented surface of genus $g$, with $g\\ \\geq \\ 2$, and let $\\mathcal X_0^{\\mathrm{good}}$ be the good locus of $\\operatorname{PU}(2,\\,1)$ representations with Toledo invariant zero. For $1\\ \\leq \\ b\\ \\leq\\ 2g-3$, we show that representations admitting an equivariant minimal map of total ramification at least $b$, for some marked complex structure, form a countable union of compact null sets of Hausdorff dimension at most $16g-16-2b$. For larger $b$, this locus is empty. Consequently, on a dense $G_δ$ subset of full measure in $\\mathcal X_0^{\\mathrm{good}}$, every nonconstant equivariant minimal map is an immersion, for every marked complex structure. On the convex cocompact locus, a dense $G_δ$ subset of full measure consists of representations admitting a finite nonempty set of marked equivariant minimal immersions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29263",
  "author_total": 3,
  "authors": [
    {
      "name": "Indranil Biswas"
    },
    {
      "name": "Satyajit Guin"
    },
    {
      "name": "Pradip Kumar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/an9h6hynsh917.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29263",
  "fulltext_url": null,
  "id": "an9h6hynsh917",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29263",
  "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.AG"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7223253637",
  "pdf_url": "https://arxiv.org/pdf/2610.29263",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/an9h6hynsh917.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29263",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29263"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Ramification and Finiteness of Equivariant Minimal Surfaces",
  "title_text": "Ramification and Finiteness of Equivariant Minimal Surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/an9h6hynsh917",
  "venue": "arXiv",
  "versions": []
}