{
  "abstract": "Let $(M^n,g)$ be complete, let $u>0$, and assume $\\operatorname{Ric}_g-α\\frac{Δ_g u}{u}g\\ge (n-1)κg$. We introduce mixed radial balls associated with the conformal metric $u^{2α}g$. For these mixed radial balls, we obtain a space-form-sharp model comparison and polynomial weighted volume growth without pointwise bounds on $u$. As applications, we give a radial derivation of the spectral Bonnet--Myers and sharp volume theorem of Antonelli--Xu, and a short volume growth derivation of the stable Bernstein theorem in $\\mathbb{R}^4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02430",
  "author_total": 2,
  "authors": [
    {
      "name": "Han Hong"
    },
    {
      "name": "Gaoming Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/06ee86f1cp6h1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02430",
  "fulltext_url": null,
  "id": "06ee86f1cp6h1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02430",
  "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.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7207871490",
  "pdf_url": "https://arxiv.org/pdf/2609.02430",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/06ee86f1cp6h1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02430",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02430"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Mixed Radial Volume Comparison under Spectral Ricci Bounds",
  "title_text": "Mixed Radial Volume Comparison under Spectral Ricci Bounds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/06ee86f1cp6h1",
  "venue": "arXiv",
  "versions": []
}