{
  "abstract": "Let $S$ be an oriented surface, possibly of infinite type, endowed with a complete Riemannian metric with pinched negative curvature. We prove that the area form defines a non-trivial class in the second bounded cohomology group of $S$, unless $S$ is diffeomorphic to the disc or the cylinder. This is in sharp contrast with the $n$-dimensional case, $n>2$, where the non-triviality of the volume form in bounded cohomology is related to the Cheeger constant of the manifold. We also discuss how the bounded area class depends on the metric: we prove that, for compact surfaces, it recognizes constant curvature metrics among pinched negatively curved ones, while, even in the case of surfaces of infinite type, it does not distinguish non-isometric hyperbolic structures. More precisely, when $S$ is compact we show that, among the negatively curved structures of fixed area, the ones with constant curvature provide the unique minimizers for the norm of the bounded area class.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01830",
  "author_total": 2,
  "authors": [
    {
      "name": "Roberto Frigerio"
    },
    {
      "name": "Ervin Hadziosmanovic"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0x1gqke3tkgkv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01830",
  "fulltext_url": null,
  "id": "0x1gqke3tkgkv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01830",
  "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.AG"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7207816577",
  "pdf_url": "https://arxiv.org/pdf/2609.01830",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0x1gqke3tkgkv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.01830",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01830"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The bounded area class of negatively curved surfaces",
  "title_text": "The bounded area class of negatively curved surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/0x1gqke3tkgkv",
  "venue": "arXiv",
  "versions": []
}