{
  "abstract": "We prove \\emph{a priori} interior $L^2$ bounds for the second fundamental form of area-minimizing currents modulo $2$ in every dimension $n\\geq 2$ and arbitrary codimension. The bounds depend only on the dimension, codimension, and an upper bound for the mass. As a corollary, we show that area-minimizing surfaces modulo $2$ with bounded area lie in finitely many diffeomorphism classes. This answers a question of \\cite{Liu2020WeakCounterexamples}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26592",
  "author_total": 1,
  "authors": [
    {
      "name": "Zachary Lihn"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bftw06tz7vpmf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26592",
  "fulltext_url": null,
  "id": "bftw06tz7vpmf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26592",
  "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.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7214120648",
  "pdf_url": "https://arxiv.org/pdf/2609.26592",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bftw06tz7vpmf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.26592",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26592"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "$L^2$ Curvature Bounds for Area-Minimizing Currents Mod(2)",
  "title_text": "L^2 Curvature Bounds for Area-Minimizing Currents Mod(2)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/bftw06tz7vpmf",
  "venue": "arXiv",
  "versions": []
}