{
  "abstract": "We show that if $(X,d,\\mathscr H^n)$ is an $RCD(K,N)$ space for some $K\\in\\mathbb{R}$ and $N\\in [1,\\infty)$, then it is also a (non-collapsed) $RCD(K,n)$ space. In other words, unweighted finite-dimensional $RCD$ spaces enjoy an automatic improvement of the dimension bound to the Hausdorff dimension of the space. More generally, we prove that this holds also when $N=\\infty$, provided that we assume in addition the $n$-rectifiability of the space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30684",
  "author_total": 2,
  "authors": [
    {
      "name": "Camillo Brena"
    },
    {
      "name": "Luca Gennaioli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0nyd0r6g3gh5b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30684",
  "fulltext_url": null,
  "id": "0nyd0r6g3gh5b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30684",
  "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"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
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  "openalex": "W7204863515",
  "pdf_url": "https://arxiv.org/pdf/2608.30684",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0nyd0r6g3gh5b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30684",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30684"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Improvement of the dimension bound for unweighted RCD spaces",
  "title_text": "Improvement of the dimension bound for unweighted RCD spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/0nyd0r6g3gh5b",
  "venue": "arXiv",
  "versions": []
}