{
  "abstract": "Given a one form $λ$ in $\\mathbb{R}^N$ and $f: \\mathbb{S}^{n} \\to \\mathbb{R}^N$ with $f^\\ast λ= 0$ we discuss the maximal Hölder regularity of extensions $F: \\mathbb{B}^{n+1} \\to \\mathbb{R}^N$ such that $F^\\astλ= 0$ in distributional sense. Our analysis applies to the Heisenberg groups $\\mathbb{H}_n$. It implies in particular that for all $n \\geq 1$ any smooth horizontal map $f: \\mathbb{S}^{n} \\to \\mathbb{H}_n$ can be extended to a $C^α$-map $F: \\mathbb{B}^{n+1} \\to \\mathbb{H}_n$ for some $α> 1/2$. Moreover, if $n \\geq 3$ we find $C^α$-embeddings from $\\mathbb{B}^{n+1}$ into $\\mathbb{H}_n$ for some $α> \\frac{1}{2}$. In the appendix we discuss an (as of now unverified) approach to extend these arguments to find $C^α$-embeddings from $\\mathbb{B}^{2}$ into $\\mathbb{H}_1$ for some $α> \\frac{1}{2}$, assisted by GPT-6 Astra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.03667",
  "author_total": 1,
  "authors": [
    {
      "name": "Armin Schikorra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/827y9vbc52thw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.03667",
  "fulltext_url": null,
  "id": "827y9vbc52thw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.03667",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7167616536",
  "pdf_url": "https://arxiv.org/pdf/2607.03667",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/827y9vbc52thw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2607.03667",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.03667"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Hölder maps under Pfaffian constraints",
  "title_text": "Hölder maps under Pfaffian constraints",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/827y9vbc52thw",
  "venue": "arXiv",
  "versions": []
}