{
  "abstract": "Let $M$ be a closed manifold equipped with a collection of smooth real vector fields $X_1,\\ldots, X_k$ and a smooth measure $μ$. Let $P:=\\sum_j X_j^\\dagger X_j $ be the associated sublaplacian. Under the assumption that each pair of points of $M$ can be connected by a path obtained by joining integral curves of the vector fields, the equation \\[ Pu=f \\] admits unique zero-average solutions $u$ in the natural energy space, for all zero average data $f\\in L^2$. We say that exact regularity holds for the above equation if $u\\in H^k(M)$ whenever $f\\in H^k(M)$, where $H^k(M)$ is the $L^2$ based Sobolev space of any order $k\\in \\mathbb{N}$. We investigate how the presence of a characteristic submanifold, namely a submanifold tangent to all vector fields $X_j$, may cause a failure of exact regularity. We prove that this indeed happens for a class of \"worm sublaplacians\", which are real analogues of Kohn Laplacians on Diederich--Fornaess worm domains, of interest in several complex variables. Our main tool is a scaling lemma inspired by work of Barrett and Christ on the $\\bar\\partial$-Neumann problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03037",
  "author_total": 1,
  "authors": [
    {
      "name": "Gian Maria Dall'Ara"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/72crkrxfzn6h1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03037",
  "fulltext_url": null,
  "id": "72crkrxfzn6h1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03037",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7220469270",
  "pdf_url": "https://arxiv.org/pdf/2610.03037",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/72crkrxfzn6h1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03037",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03037"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Obstructions to exact regularity of sublaplacians",
  "title_text": "Obstructions to exact regularity of sublaplacians",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/72crkrxfzn6h1",
  "venue": "arXiv",
  "versions": []
}