{
  "abstract": "Let $Ω\\subset\\mathbb{R}^n$ be a domain, with $n\\ge2$. We characterize the real-valued harmonic functions that can occur as prescribed real components of monogenic functions. For any fixed nonzero real Clifford module $M$ and any fixed unit vector $s\\in M$, a smooth real-valued function $h$ can be written as $h=\\langle F,s\\rangle$ with $F$ monogenic if and only if the $(n-1)$-form $*dh$ is exact. Consequently, every real-valued harmonic function on $Ω$ admits such a representation if and only if $H_{\\mathrm{dR}}^{n-1}(Ω)=0$. In dimension eight, the same exactness criterion characterizes the real parts of octonionic regular functions and yields the corresponding equivalence with $H_{\\mathrm{dR}}^7(Ω)=0$. The proofs use global solvability of the Poisson equation and elementary identities for differential forms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30648",
  "author_total": 2,
  "authors": [
    {
      "name": "Yong Li"
    },
    {
      "name": "Yuchen Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f8w8zxe7qpr0y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30648",
  "fulltext_url": null,
  "id": "f8w8zxe7qpr0y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30648",
  "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.CV"
    ],
    [
      "openalex",
      "2604|Algebraic and Geometric Analysis"
    ]
  ],
  "openalex": "W7223276911",
  "pdf_url": "https://arxiv.org/pdf/2610.30648",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f8w8zxe7qpr0y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30648",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30648"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Octonionic and Monogenic Completions of Harmonic Functions",
  "title_text": "Octonionic and Monogenic Completions of Harmonic Functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/f8w8zxe7qpr0y",
  "venue": "arXiv",
  "versions": []
}