{
  "abstract": "Let $I_{\\inf}(a):=\\lim_{n\\to\\infty}I_{n}(a)=\\inf_{n\\ge1}I_{n}(a)$ be the asymptotic isoperimetric profile for product of a weighted Riemannian manifold satisfying $\\mathrm{CD}(0,\\infty)$ and, more broadly, for product of a nonsmooth subspace with density that can be approximated by a sequence of densities satisfying $\\mathrm{CD}(0,\\infty)$. We establish the following identity: \\[ \\lim_{a\\downarrow0}\\frac{I_{\\inf}(a)}{a\\sqrt{2\\ln(1/a)}}=\\sqrt{K_{\\mathrm{LS}}}, \\] where $K_{\\mathrm{LS}}$ is the optimal log-Sobolev constant. The same argument also yields the large-deviation and moderate-deviation asymptotics for isoperimetry.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23537",
  "author_total": 1,
  "authors": [
    {
      "name": "Lei Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cq5nap69z0qp1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23537",
  "fulltext_url": null,
  "id": "cq5nap69z0qp1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23537",
  "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"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7214023149",
  "pdf_url": "https://arxiv.org/pdf/2609.23537",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cq5nap69z0qp1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23537",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23537"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Sharp Small-Volume Isoperimetry from Log-Sobolev Inequalities",
  "title_text": "Sharp Small-Volume Isoperimetry from Log-Sobolev Inequalities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/cq5nap69z0qp1",
  "venue": "arXiv",
  "versions": []
}