{
  "abstract": "Let \\(G\\) be a finite group acting on a connected open Riemann surface \\(X\\) by holomorphic automorphisms and acting on a Euclidean space \\(\\mathbb R^n\\), \\(n\\ge 3\\), by orthogonal transformations. In a previous paper, the second author gave a necessary and sufficient condition for the existence of a \\(G\\)-equivariant conformal minimal immersion \\(F:X\\to\\mathbb R^n\\), and he asked whether such \\(F\\) can be chosen to be a proper map. Assuming that this condition holds, we give an affirmative answer when \\(X\\) is a bordered Riemann surface and \\(G\\) acts freely on the boundary of \\(X\\). This contributes to the Sullivan conjecture concerning the existence of proper hyperbolic minimal surfaces in \\(\\mathbb R^3\\) of finite topology. Under the same conditions, we also construct a \\(G\\)-equivariant proper conformal minimal immersion of \\(X\\) to the unit ball of \\(\\mathbb R^n\\) which is complete in the induced metric, thereby opening a new direction in the Calabi--Yau theory regarding the study of complete bounded minimal surfaces. Analogous results hold for null curves in \\(\\mathbb C^n\\).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31847",
  "author_total": 2,
  "authors": [
    {
      "name": "Antonio Alarcon"
    },
    {
      "name": "Franc Forstneric"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7pxza5k1a65yt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31847",
  "fulltext_url": null,
  "id": "7pxza5k1a65yt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31847",
  "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.CV"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7223688703",
  "pdf_url": "https://arxiv.org/pdf/2610.31847",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7pxza5k1a65yt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.31847",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31847"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Calabi-Yau and Sullivan conjectures for minimal surfaces with symmetries",
  "title_text": "The Calabi-Yau and Sullivan conjectures for minimal surfaces with symmetries",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/7pxza5k1a65yt",
  "venue": "arXiv",
  "versions": []
}