{
  "abstract": "Let Ric_g = Λg, where Λ > 0. For Einstein warped products of closed manifolds, we prove that the least transverse-traceless Einstein eigenvalue is strictly less than −(n−2)Λ/(n−1), without an upper bound on the dimension. The same estimate holds for the smooth spherical-fibre completions specified here, unless the completed metric is round. A trace-free Hessian correction expresses the shifted quadratic form as a negative sum of squared base-curvature tensors and admits an H¹ extension across the collapsing fibres. In dimension four, there is a universal positive gap for ‖(λ_max(W⁺)−2Λ/3)_+‖_{L²} on closed simply connected oriented positive Einstein manifolds. Below this gap the excess vanishes, and the metric is anti-self-dual or Kähler–Einstein in the given orientation. The proof uses Einstein orbifold compactness, extension of parallel real line bundles through anti-self-dual ALE limits, and LeBrun–Ozuch’s Kähler–Einstein desingularization theorem. For circle-warped four-metrics, the corrected quadratic form equals a negative multiple of either chiral Weyl energy. The small-excess TT-semistable metrics are the round sphere and the Fubini–Study plane. Preprint. MSC 2020: 53C25, 58J50, 53C23.Author manuscript: https://anassnifa.com/papers/einstein-instability-weyl-gap",
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  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Anass Nifa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/42h7k0rr7y7fe.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.22851382",
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  "id": "42h7k0rr7y7fe",
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  "landing_url": "https://hal.science/hal-05769881v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "metadata_licence": null,
  "native_subjects": [
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  "pdf_url": "https://hal.science/hal-05769881/document",
  "pmcid": null,
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  "published": "2026-09-01",
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  "ris": "https://research.draconitic.com/paper/42h7k0rr7y7fe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:43Z",
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-dg",
      "subfield": "geometry-topology"
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  "title": "Instability of Einstein warped products and a one-sided Weyl curvature gap",
  "title_text": "Instability of Einstein warped products and a one-sided Weyl curvature gap",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:43Z",
  "url": "https://research.draconitic.com/paper/42h7k0rr7y7fe",
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}