{
  "abstract": "In this article, we investigate spectral properties of compact $V$-static manifolds, namely, compact manifolds with boundary whose metrics are critical points of the volume functional under a scalar curvature constraint. We derive sharp estimates for the first Steklov eigenvalue and the entire fourth-order Steklov spectrum. We further obtain a Lichnerowicz-type lower bound for the first eigenvalue of the drifted Laplacian naturally associated with the $V$-static potential. In the corresponding equality cases, we obtain rigidity results characterizing the Euclidean ball and the hemisphere.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18717",
  "author_total": 3,
  "authors": [
    {
      "name": "Rafael Diógenes"
    },
    {
      "name": "Jaciane Gonçalves"
    },
    {
      "name": "Ernani Ribeiro Jr"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3jbdba4dbk17a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18717",
  "fulltext_url": null,
  "id": "3jbdba4dbk17a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18717",
  "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.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7213518689",
  "pdf_url": "https://arxiv.org/pdf/2609.18717",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3jbdba4dbk17a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.18717",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18717"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Spectral properties for critical metrics of the volume functional",
  "title_text": "Spectral properties for critical metrics of the volume functional",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/3jbdba4dbk17a",
  "venue": "arXiv",
  "versions": []
}