{
  "abstract": "We establish sharp quantitative stability of the Ashbaugh--Benguria inequality on bounded convex domains in $\\mathbb R^n$. After volume and centroid normalization, the eigenvalue-ratio deficit controls the squared $H^{-1/2}(\\mathbb S^{n-1})$ norm of the radial displacement from the unit sphere. This yields the optimal exponent $5/2$ for the Fraenkel asymmetry and, for small deficits, the optimal exponent $(n+4)/2$ for the normalized Hausdorff distance. All three exponents are sharp even among smooth strictly convex domains whose principal curvatures lie in $[1/2,2]$. In particular, the quadratic Fraenkel-asymmetry estimate proposed by Brasco and De Philippis (2017, Open Problem 7.65) fails. We also determine the optimal stability exponents under higher-order radial regularity bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31223",
  "author_total": 3,
  "authors": [
    {
      "name": "Long-Han Huang"
    },
    {
      "name": "Yuxuan Zhou"
    },
    {
      "name": "Wenming Zou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/em6e0t8hw0kkf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31223",
  "fulltext_url": null,
  "id": "em6e0t8hw0kkf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31223",
  "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",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7223352854",
  "pdf_url": "https://arxiv.org/pdf/2610.31223",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/em6e0t8hw0kkf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31223",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31223"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp quantitative stability of the Ashbaugh--Benguria inequality",
  "title_text": "Sharp quantitative stability of the Ashbaugh--Benguria inequality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/em6e0t8hw0kkf",
  "venue": "arXiv",
  "versions": []
}