{
  "abstract": "This paper is the second in a series by the author and collaborators devoted to the study of geometric and analytic properties of nonlinear Lebesgue spaces, that is, L^p spaces of mappings taking values in arbitrary metric spaces. The present article formalizes the pointwise description of their geometric properties---their length structure, bounds on their Alexandrov curvature as well as the definition of a velocity for absolutely continuous curves despite the lack of differential structure. To obtain this pointwise description, we first prove a nonlinear analogue of the Fubini--Lebesgue theorem, which yields an identification of L^p curves in nonlinear Lebesgue spaces with mappings taking values in the space of L^p curves. This identification of L^p curves then enables a similar identification for absolutely continuous curves, from which the pointwise description of the geometric properties of nonlinear Lebesgue spaces follows.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2603.09459",
  "author_total": 1,
  "authors": [
    {
      "name": "Guillaume Sérieys"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9cv3wtffmc65k.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "9cv3wtffmc65k",
  "issns": [],
  "landing_url": "https://hal.science/hal-05544460v4",
  "language": "en",
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-dg"
    ],
    [
      "hal",
      "1.math.math-fa"
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      "hal",
      "1.math.math-mg"
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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05544460/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9cv3wtffmc65k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:51Z",
      "native_id": "hal-05544460",
      "source": "hal",
      "url": "https://hal.science/hal-05544460v4"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-fa",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-dg",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Nonlinear Lebesgue spaces: Curves and geometry",
  "title_text": "Nonlinear Lebesgue spaces: Curves and geometry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:51Z",
  "url": "https://research.draconitic.com/paper/9cv3wtffmc65k",
  "venue": "HAL",
  "versions": []
}