{
  "abstract": "The horizontal mean curvature flow is a geometric evolution associated with the horizontal perimeter in sub-Riemannian spaces. In this paper, we introduce a minimizing movement scheme for this flow in the first Heisenberg group $\\mathbb{H}$, and prove the existence of a flat flow which is locally $1/2$-Hölder continuous in time, with respect to the $L^1$-distance. The construction applies to arbitrary bounded sets of finite horizontal perimeter and does not require smoothness or symmetry of the initial datum.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20054",
  "author_total": 3,
  "authors": [
    {
      "name": "A. Cesaroni"
    },
    {
      "name": "M. Novaga"
    },
    {
      "name": "P. Pozzi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0vfezcxk59ngw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20054",
  "fulltext_url": null,
  "id": "0vfezcxk59ngw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20054",
  "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.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7222229847",
  "pdf_url": "https://arxiv.org/pdf/2610.20054",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0vfezcxk59ngw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.20054",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20054"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A semi-discrete scheme for horizontal mean curvature flow in the Heisenberg group",
  "title_text": "A semi-discrete scheme for horizontal mean curvature flow in the Heisenberg group",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/0vfezcxk59ngw",
  "venue": "arXiv",
  "versions": []
}