{
  "abstract": "Let $M$ be a closed manifold of arbitrary dimension. The length spectrum of a negatively curved metric $g$ on $M$ is the set of lengths of all possible closed geodesics of $g$. We prove that metrics whose length spectrum is exponentially sparse, i.e., the gaps between distinct lengths are bounded below by a quantity decaying exponentially in the length, are prevalent, and hence dense, among $C^k$-smooth negatively curved metrics on $M$ for sufficiently large $k$. Moreover, unlike in all known constructions, the exponent in our bound grows only sublinearly in the regularity $k$. This work is motivated by our recent result on prevalent unmarked length spectral rigidity for expanding circle maps and a very recent result by DeWitt, Durham, Reber, and O'Hare that $C^k$-smooth negatively curved metrics with exponentially sparse spectra are locally rigid.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12351",
  "author_total": 2,
  "authors": [
    {
      "name": "Kostiantyn Drach"
    },
    {
      "name": "Vadim Kaloshin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0vg11dq5p15nb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12351",
  "fulltext_url": null,
  "id": "0vg11dq5p15nb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12351",
  "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.DG"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7221069123",
  "pdf_url": "https://arxiv.org/pdf/2610.12351",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0vg11dq5p15nb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12351",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12351"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Prevalence of sparsity for negatively curved metrics",
  "title_text": "Prevalence of sparsity for negatively curved metrics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/0vg11dq5p15nb",
  "venue": "arXiv",
  "versions": []
}