{
  "abstract": "We prove the generalized Cartan-Hadamard conjecture, also known as the Aubin conjecture, in the small volume regime under a lower Ricci curvature bound, for any dimension $n\\geq 2$. More precisely, we show that if $(M^n,g)$ is a Cartan-Hadamard manifold satisfying $\\mathrm{Sec}_g\\leq\\bar k\\leq 0$ and $\\mathrm{Ric}_g\\geq (n-1)\\underline k$, then its isoperimetric profile is at least that of the model space of curvature $\\bar k$ for small enough volumes. We also reduce the proof of the generalized Cartan-Hadamard conjecture to establishing rigidity in the equality case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17093",
  "author_total": 4,
  "authors": [
    {
      "name": "Marcos Agnoletto"
    },
    {
      "name": "Márcio Fabiano Da Silva"
    },
    {
      "name": "Stefano Nardulli"
    },
    {
      "name": "Reinaldo Resende"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/efg3avw64t39d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17093",
  "fulltext_url": null,
  "id": "efg3avw64t39d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17093",
  "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": "W7213415861",
  "pdf_url": "https://arxiv.org/pdf/2609.17093",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/efg3avw64t39d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2609.17093",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17093"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A proof of the Cartan-Hadamard conjecture for small volumes under a Ricci curvature lower bound",
  "title_text": "A proof of the Cartan-Hadamard conjecture for small volumes under a Ricci curvature lower bound",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/efg3avw64t39d",
  "venue": "arXiv",
  "versions": []
}