{
  "abstract": "We construct an explicit length-minimizing curve in a polynomial rank-two sub-Riemannian structure on $\\R^4$. Its arclength parametrization is $C^{1,1/2}$ and is not $C^{1,α}$ near an interior point for any $α>1/2$. Minimality is proved by an approximate calibration chosen separately for each competitor. The example admits a minimizing lift to a rank-two Carnot group of step five. Generalizations are announced.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38481",
  "author_total": 3,
  "authors": [
    {
      "name": "Nicola Cavallucci"
    },
    {
      "name": "Enrico Le Donne"
    },
    {
      "name": "Sebastiano Nicolussi Golo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/27vnyvb85n0kr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38481",
  "fulltext_url": null,
  "id": "27vnyvb85n0kr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38481",
  "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.DG"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38481",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/27vnyvb85n0kr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38481",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38481"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Carnot geodesics with Hölder controls",
  "title_text": "Carnot geodesics with Hölder controls",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/27vnyvb85n0kr",
  "venue": "arXiv",
  "versions": []
}