{
  "abstract": "We prove a sharp comparison, with Obata-type rigidity, for all Neumann eigenvalues of one-dimensional $\\mathrm{CD}(1,2)$ spaces against the Legendre model, under a convexity condition on the density. It follows that minimizers of the $k$-th Laplace eigenvalue among closed surfaces of Gaussian curvature at least $1$ cannot collapse in the measured Gromov-Hausdorff completion, for every $k\\ge2$. We also give a variational proof that smooth minimizers are round.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02808",
  "author_total": 1,
  "authors": [
    {
      "name": "Aditya Tiwari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d7kta17j0gntx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02808",
  "fulltext_url": null,
  "id": "d7kta17j0gntx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02808",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7207868826",
  "pdf_url": "https://arxiv.org/pdf/2609.02808",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d7kta17j0gntx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02808",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02808"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Minimizers of Laplace eigenvalues under a lower curvature bound",
  "title_text": "Minimizers of Laplace eigenvalues under a lower curvature bound",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/d7kta17j0gntx",
  "venue": "arXiv",
  "versions": []
}