{
  "abstract": "We study eigenvalues and eigenfunctions of the ``div-grad type\" sub-Laplacian with respect to Popp's volume on a compact equiregular sub-Riemannian manifold $M$. Since Popp's volume is canonically determined by the sub-Riemannian structure of $M$, the spetra of the sub-Laplacian carry geometric meanings. In this paper, we first embed $M$ into the Hilbert space of square-summable sequences using eigenfunctions and then define a spectral distance between two compact equiregular sub-Riemannian manifolds. Our result is a sub-Riemannian analogue of Berard-Besson-Gallot's classical work in the Riemannian case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.12804",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuzuru Inahama"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dcgpx4xa7kj03.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.12804",
  "fulltext_url": null,
  "id": "dcgpx4xa7kj03",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.12804",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7164547020",
  "pdf_url": "https://arxiv.org/pdf/2606.12804",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dcgpx4xa7kj03.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2606.12804",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.12804"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Sub-Riemannian spectral distance",
  "title_text": "Sub-Riemannian spectral distance",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/dcgpx4xa7kj03",
  "venue": "arXiv",
  "versions": []
}