{
  "abstract": "We prove the existence of arbitrarily high-dimensional families of minimal surfaces of any prescribed genus and conformal structure in even-dimensional round spheres. More precisely, let $n\\geq2$ and let $Σ$ be any closed Riemann surface of genus $g$. We construct a sequence of degrees $d_\\ell\\to+\\infty$ such that, for every $\\ell$, there exists a complex manifold of complex dimension $2d_\\ell+n^2(1-g)$ consisting of linearly full branched superminimal immersions of $Σ$ into $\\mathbb S^{2n}$ of degree $d_\\ell$. In particular, this yields parametrized families of linearly full branched minimal immersions whose dimensions tend to infinity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09016",
  "author_total": 1,
  "authors": [
    {
      "name": "Riccardo Caniato"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/22xakmw3ztekq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09016",
  "fulltext_url": null,
  "id": "22xakmw3ztekq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09016",
  "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.AP"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212074530",
  "pdf_url": "https://arxiv.org/pdf/2609.09016",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/22xakmw3ztekq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.09016",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09016"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "High-Dimensional Families of Minimal Surfaces of Arbitrary Genus in Round Spheres",
  "title_text": "High-Dimensional Families of Minimal Surfaces of Arbitrary Genus in Round Spheres",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/22xakmw3ztekq",
  "venue": "arXiv",
  "versions": []
}