{
  "abstract": "Banach asked in 1932 whether a real Banach space $X$ whose $n$-dimensional subspaces, for some fixed $1<n<\\dim X$, are all linearly isometric must be a Hilbert space. Gromov proved the conjecture for even $n$, and subsequent work settled several odd-dimensional cases. We prove the conjecture for every odd $n$, including all previously unresolved cases. Together with Gromov's result for even $n$, this completes Banach's isometric conjecture in the real case. The proof combines principal bundle theory with a Brouwer degree argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.13536",
  "author_total": 2,
  "authors": [
    {
      "name": "Xinbao Lu"
    },
    {
      "name": "Kaiwen Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9nc91wm72yc78.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.13536",
  "fulltext_url": null,
  "id": "9nc91wm72yc78",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.13536",
  "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.FA"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7203450684",
  "pdf_url": "https://arxiv.org/pdf/2608.13536",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9nc91wm72yc78.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.13536",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.13536"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A solution to Banach's isometric conjecture",
  "title_text": "A solution to Banach's isometric conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/9nc91wm72yc78",
  "venue": "arXiv",
  "versions": []
}