{
  "abstract": "We prove that, in most moduli spaces of orientable hyperbolic surfaces of finite area, there exist surfaces all of whose covers of degree two have a new small eigenvalue. On the other hand, we show that four punctured spheres always admit a double cover without new small eigenvalues and that there exist closed surfaces of any genus with the same property. We prove the last two of these results using a version of Cheeger's inequality adapted to double covers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07193",
  "author_total": 2,
  "authors": [
    {
      "name": "Lawford Hatcher"
    },
    {
      "name": "Bram Petri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/44a90w2vv7w9m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07193",
  "fulltext_url": null,
  "id": "44a90w2vv7w9m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07193",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
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      "arxiv",
      "math.GN"
    ],
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      "2610|Spectral Theory in Mathematical Physics"
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  "openalex": "W7220934900",
  "pdf_url": "https://arxiv.org/pdf/2610.07193",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/44a90w2vv7w9m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07193",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07193"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Spectral gaps of double covers of hyperbolic surfaces",
  "title_text": "Spectral gaps of double covers of hyperbolic surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/44a90w2vv7w9m",
  "venue": "arXiv",
  "versions": []
}