{
  "abstract": "Let $(M^n,g)$, $n\\ge2$, be a compact connected Riemannian manifold with smooth nonempty boundary, $\\operatorname{Ric}_M\\ge(n-1)Kg$ for $K>0$, and nonnegative outward boundary mean curvature. We derive an explicit algebraic lower bound $B_η$ for the first Dirichlet eigenvalue from Kasue's mixed inradius model. With $R$ the inradius and $s=4KR^2/π^2$, the bound involves one square root and approximates the model eigenvalue with relative error $O_n(s^4)$ as $s\\downarrow0$ for fixed $n$. The construction uses the first two moments of a positive representation of the averaged model potential and a sharp pointwise corrector estimate. For the chosen spectral transfer, the first two moments determine an optimal bound. We also show that the model eigenvalue is the geometric infimum at fixed $(n,K,R)$. For $0<s<1$, it is approached by smooth collapsing balls with sectional curvature at least $K$ and totally geodesic boundary. At the maximal inradius, the model value is attained by the round hemisphere. The bound strictly improves the variance refinement throughout $0<s\\le1$. We also give a direct algebraic comparison with an optimized power-test benchmark.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14069",
  "author_total": 1,
  "authors": [
    {
      "name": "Thomas Schürmann"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ac39cxc94q76.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14069",
  "fulltext_url": null,
  "id": "2ac39cxc94q76",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14069",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7221785996",
  "pdf_url": "https://arxiv.org/pdf/2610.14069",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ac39cxc94q76.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.14069",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14069"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "An Explicit Bound for the First Dirichlet Eigenvalue via Two Moments",
  "title_text": "An Explicit Bound for the First Dirichlet Eigenvalue via Two Moments",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/2ac39cxc94q76",
  "venue": "arXiv",
  "versions": []
}