{
  "abstract": "This paper investigates the theory of fractional Sobolev mappings between Carnot groups, with a particular focus on the Korevaar-Schoen energy functional and interpolation properties. We establish that weak contact equations hold for fractional Sobolev mappings on Carnot groups, generalizing classical results from the Euclidean setting to the sub-Riemannian framework. Our main results include: (1) the proof that fractional Sobolev mappings satisfying weak contact equations belong to the horizontal fractional Sobolev space $W_H^{s-λ,q}(Ω;G_2)$ for any sufficiently small $λ>0$; (2) interpolation theorems for fractional Sobolev mappings between Carnot groups, demonstrating that the limiting behavior as $s \\to 1$ recovers the first-order Sobolev space; (3) a rigorous treatment of the Korevaar-Schoen energy on Carnot groups, including a characterization of its minimizers via horizontal differential forms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10551",
  "author_total": 1,
  "authors": [
    {
      "name": "Yihan Cui"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f21djjmpgv9nm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10551",
  "fulltext_url": null,
  "id": "f21djjmpgv9nm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10551",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7221078679",
  "pdf_url": "https://arxiv.org/pdf/2610.10551",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f21djjmpgv9nm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.10551",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10551"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Korevaar-Schoen Energy and Interpolations of Fractional Sobolev mappings on Carnot groups",
  "title_text": "Korevaar-Schoen Energy and Interpolations of Fractional Sobolev mappings on Carnot groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/f21djjmpgv9nm",
  "venue": "arXiv",
  "versions": []
}