{
  "abstract": "In this work, a sharp Kähler spectral almost-rigidity theorem was established, resolving Conjecture 1.8 of Chu--Wang--Zhang. For compact Kähler manifolds satisfying $\\Ric(ω)\\geqω$, pinching the first $n^2+3$ nonzero complex eigenvalues to one forces the manifolds to be Gromov Hausdorff close to normalized complex projective space and determines the biholomorphism type. The smaller index $n^2+1$ is the sharp threshold for noncollapsing. More generally, if a normalized measured limit has essential real dimension $r$, then the multiplicity of the critical eigenvalue is at most $r+\\lfloor r/2\\rfloor^2$, with equality attained in every dimension. A uniform energy estimate for kernel projections of complex gradient Gram matrices leads to a Lie algebra action on the whole spectral resolution.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12525",
  "author_total": 1,
  "authors": [
    {
      "name": "Haohao Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cgs793n41bgd7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12525",
  "fulltext_url": null,
  "id": "cgs793n41bgd7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12525",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7213026378",
  "pdf_url": "https://arxiv.org/pdf/2609.12525",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cgs793n41bgd7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12525",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12525"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Spectral almost rigidity on Kähler manifolds with positive Ricci lower bound",
  "title_text": "Spectral almost rigidity on Kähler manifolds with positive Ricci lower bound",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/cgs793n41bgd7",
  "venue": "arXiv",
  "versions": []
}