{
  "abstract": "We establish quantitative stability for radial Caffarelli-Kohn-Nirenberg inequalities involving the anisotropic radial derivative and the Minkowski functional of a smooth, strictly convex body in $\\mathbb R^N$, $N\\ge2$. Here, the convex body need not be origin-symmetric. For the $L^2$-Caffarelli-Kohn-Nirenberg inequality, we establish the sharp stability constant $|b+1-a|$ for $a\\ne b+1$, and classify all equality cases in the natural weighted completion spaces, by optimizing over the angular coefficients and a common dilation parameter. We also obtain the sharp stability constants $2$ and $4$ for the scale-invariant and scale-noninvariant $L^2$-Heisenberg inequality, respectively. For $2\\le p<\\infty$, we also establish weighted stability of the anisotropic radial $L^p$-Caffarelli-Kohn-Nirenberg inequalities when $a\\neq b+1$ and $(b+1-a)(N-p(b+1))\\geq0$, and the anisotropic radial $L^p$-Heisenberg inequalities. As a byproduct, we establish weighted $L^p$-Poincaré inequalities for Gamma measures, which serve as the main tool for our stability estimates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40360",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhenzhen Wei"
    },
    {
      "name": "Denghui Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9fyv9n0n4nhxz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40360",
  "fulltext_url": null,
  "id": "9fyv9n0n4nhxz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40360",
  "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.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40360",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9fyv9n0n4nhxz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40360",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40360"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp $L^2$ stability for anisotropic radial Caffarelli-Kohn-Nirenberg inequalities",
  "title_text": "Sharp L^2 stability for anisotropic radial Caffarelli-Kohn-Nirenberg inequalities",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:51Z",
  "url": "https://research.draconitic.com/paper/9fyv9n0n4nhxz",
  "venue": "arXiv",
  "versions": []
}