{
  "abstract": "Let $(M^n,g_0)$ be a closed hyperbolic manifold, $n\\geq3$. We compute the Hessian of volume entropy at $g_0$ under the constraint $Sc_g=-n(n-1)$ and express it as a quadratic form on transverse-traceless symmetric two-tensors. In dimension three, the Hessian is negative definite, and every sufficiently $C^\\infty$-close metric with $Sc_g\\geq-6$ has entropy at most $2$, with equality precisely for pullbacks of $g_0$. In dimensions $n\\geq4$, a universal spectral threshold determines the Hessian sign. Nonzero trace-free Codazzi tensors give positive directions, and hyperbolic bending provides smooth constrained entropy saddles in every such dimension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06466",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiaodong Wang"
    },
    {
      "name": "Bo Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/512anbs51dvgh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06466",
  "fulltext_url": null,
  "id": "512anbs51dvgh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06466",
  "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.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7220666711",
  "pdf_url": "https://arxiv.org/pdf/2610.06466",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/512anbs51dvgh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06466",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06466"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Volume Entropy and Scalar Curvature near a Hyperbolic Metric",
  "title_text": "Volume Entropy and Scalar Curvature near a Hyperbolic Metric",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/512anbs51dvgh",
  "venue": "arXiv",
  "versions": []
}