{
  "abstract": "We find bounds for the genus and for the number of boundary components of a surface that is either index one as a free boundary minimal surface or stable as a free boundary constant mean curvature surface in a Riemannian three-manifold with convex boundary and non-negative Ricci curvature, provided the first Dirichlet eigenvalue of its Jacobi operator is non-negative. As an application, we establish strong topological restrictions on such surfaces in compact strictly convex domains of three-dimensional normal homogeneous spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31304",
  "author_total": 2,
  "authors": [
    {
      "name": "Alcides de Carvalho"
    },
    {
      "name": "Roney Santos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0knxqrpavjqjc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31304",
  "fulltext_url": null,
  "id": "0knxqrpavjqjc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31304",
  "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.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7214635507",
  "pdf_url": "https://arxiv.org/pdf/2609.31304",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0knxqrpavjqjc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31304",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31304"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Topology and Dirichlet spectrum of free boundary minimal and CMC surfaces",
  "title_text": "Topology and Dirichlet spectrum of free boundary minimal and CMC surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/0knxqrpavjqjc",
  "venue": "arXiv",
  "versions": []
}