{
  "abstract": "We prove that every convex body $K\\subset\\mathbb{R}^n$ admits $S\\in\\mathrm{SL}_n(\\mathbb{R})$ such that $λ_1(SK)|K|^{2/n}\\le Cn$, where $C$ is universal. For origin-symmetric bodies of volume one, the bound holds in maximal Gaussian measure position. The main step is the spectral estimate \\[ λ_1(D)\\le C(P)\\bigl(n+\\sqrt{n I(ν\\midγ_n)}\\bigr) \\] for an even isotropic log-concave probability measure $ν$ supported on a symmetric convex body $D$, with Poincaré constant at most $P$ and finite relative Fisher information. A second-order Stein estimate and an information jump under convolution give entropy decay faster than $m^{-1}$ for normalised sums. Their supports control the Gaussian measure of dilates, and a Brownian bridge expansion gives the spectral estimate. A Gaussian-weighted ground state supplies a measure whose Fisher information is bounded in terms of $λ_1(K)$. The square-root dependence then gives the bound of order $n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02279",
  "author_total": 2,
  "authors": [
    {
      "name": "Matthew J. Colbrook"
    },
    {
      "name": "George Stepaniants"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ettwcrdxj515x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02279",
  "fulltext_url": null,
  "id": "ettwcrdxj515x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02279",
  "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.FA"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "arxiv",
      "math.SP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02279",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ettwcrdxj515x.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02279",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02279"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "An affine reverse Faber-Krahn inequality via information decay",
  "title_text": "An affine reverse Faber-Krahn inequality via information decay",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/ettwcrdxj515x",
  "venue": "arXiv",
  "versions": []
}