{
  "abstract": "Let $γ\\subset\\mathbb R^{m},\\,m\\geq2,$ be a closed curve of length $2π$ with its curvature $κ$, parametrized by arc length, and let $λ_γ$ be the first eigenvalue of the periodic curvature Schrödinger operator $-d^2/d s^2+κ(s)^2$. We obtain \\[ λ_γ\\geq \\frac{\\sqrtπ}{2} \\left(\\frac{Γ(7/6)}{Γ(5/3)}\\right)^3. \\] This is a near-sharp lower bound for the Ovals problem. Our proof introduces a new geometric approach. We derive a convolution identity from the closure condition and combine it with projection averaging over tangent directions and sharp Poincaré inequalities on antipodal arcs. As applications, we provide an improved two-state kinetic Lieb-Thirring inequality and the corresponding two-eigenvalue constant.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10775",
  "author_total": 1,
  "authors": [
    {
      "name": "Durvudkhan Suragan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8rahykjr11rgk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10775",
  "fulltext_url": null,
  "id": "8rahykjr11rgk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10775",
  "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.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7212241717",
  "pdf_url": "https://arxiv.org/pdf/2609.10775",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8rahykjr11rgk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.10775",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10775"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "An Improved Bound for the Ovals Problem",
  "title_text": "An Improved Bound for the Ovals Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/8rahykjr11rgk",
  "venue": "arXiv",
  "versions": []
}