{
  "abstract": "We prove scalar and tensor eigenvalue estimates for conformally Kähler Einstein four-manifolds. For the Chen–LeBrun–Weber metric, $\\operatorname{Ric}_g=\\Lambda g$, the first positive scalar eigenvalue satisfies $4\\Lambda/3\\lt \\lambda_1^{\\mathrm{sc}}(g)\\lt 1951\\Lambda/1000$. Thus this metric admits a destabilizing conformal variation, as asserted in Hall–Murphy's Conjecture 5.3. The upper bound follows from boundary moments of an affine quotient on the moment polygon and a positive-coefficient polynomial identity. For any closed Einstein four-manifold conformal to a positive-scalar-curvature Kähler metric, put $m=b_2^-\\gt 0$ and $\\rho=\\max s_k/\\min s_k$, using the complex orientation. We prove $\\lambda_m^{\\mathrm{TT}}\\le(4\\Lambda/3)(1-\\rho^{-3})$ for the full Lichnerowicz operator, with strict inequality for a nonconstant conformal factor. For the Chen–LeBrun–Weber metric, this gives two TT eigenvalues below $7\\Lambda/6$, proves the instability of its normalized Ricci-flat cone, and, together with the scalar bound, gives at least three positive directions for the entropy Hessian modulo diffeomorphisms and scaling. Finally, under $\\det W^+\\ge0$, the stable cones over closed oriented positive Einstein four-manifolds are precisely those over the round sphere and the Fubini–Study projective plane.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Anass Nifa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fv1v5ndw7bf2f.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.22851442",
  "fulltext_url": null,
  "id": "fv1v5ndw7bf2f",
  "issns": [],
  "landing_url": "https://hal.science/hal-05769995v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-dg"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05769995/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fv1v5ndw7bf2f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:43Z",
      "native_id": "hal-05769995",
      "source": "hal",
      "url": "https://hal.science/hal-05769995v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-dg",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Scalar and tensor eigenvalue bounds for conformally Kähler Einstein four-manifolds",
  "title_text": "Scalar and tensor eigenvalue bounds for conformally Kähler Einstein four-manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:43Z",
  "url": "https://research.draconitic.com/paper/fv1v5ndw7bf2f",
  "venue": "HAL",
  "versions": []
}