{
  "abstract": "Let $M$ be a closed manifold with fundamental group $G$. A subset of conjugacy classes $E \\subset \\text{conj}(G)$ is said to be spectrally rigid if when two negatively curved Riemannian metrics have the same marked length spectra on $E$, then their length spectra agree on all conjugacy classes. In this work we study spectrally rigid subsets from a quantitative perspective. We show that, if the density of $E \\subset \\text{conj}(G)$, measured with respect to a fixed reference metric, decays more slowly than $T^{-1/2}$ then $E$ is spectrally rigid. We establish analogous rigidity results for Culler-Vogtmann Outer Space and show that the $T^{-1/2}$ threshold is sharp in this setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00285",
  "author_total": 1,
  "authors": [
    {
      "name": "Stephen Cantrell"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ee8g1gdce3rj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00285",
  "fulltext_url": null,
  "id": "3ee8g1gdce3rj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00285",
  "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.GT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00285",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ee8g1gdce3rj.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00285",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00285"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Quantitative spectral rigidity for negatively curved manifolds and Outer Space",
  "title_text": "Quantitative spectral rigidity for negatively curved manifolds and Outer Space",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/3ee8g1gdce3rj",
  "venue": "arXiv",
  "versions": []
}