{
  "abstract": "We study heat content and spectral properties of subordinated sub-Laplacians on arbitrary Carnot groups. We consider restrictions of such operators to bounded open sets with zero Dirichlet boundary condition and study their spectral properties. In particular, for a large class of subordinators we give explicit eigenvalue estimates in terms of the subordinator and the eigenvalues of the sub-Laplacian. We also provide large-time asymptotics of the heat content for the subordinated sub-Laplacian in terms of its spectral gap. For fractional sub-Laplacians we prove short-time asymptotics for the corresponding heat content and relative heat content. Our approach combines semigroup methods, probabilistic techniques, geometric measure theory, and heat kernel estimates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04045",
  "author_total": 4,
  "authors": [
    {
      "name": "Maria Gordina"
    },
    {
      "name": "Liangbing Luo"
    },
    {
      "name": "Andrea Pinamonti"
    },
    {
      "name": "Rohan Sarkar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cb9ahbvq4xv47.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04045",
  "fulltext_url": null,
  "id": "cb9ahbvq4xv47",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04045",
  "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.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.04045",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cb9ahbvq4xv47.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.04045",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04045"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Heat content and spectrum for subordinated sub-Laplacians",
  "title_text": "Heat content and spectrum for subordinated sub-Laplacians",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/cb9ahbvq4xv47",
  "venue": "arXiv",
  "versions": []
}