{
  "abstract": "A complete classification is established for continuous, SL($n$) contravariant, and translation invariant tensor valuations defined on the Sobolev space $W^{1,p}(\\mathbb R^n)$. When these valuations are further assumed to be homogeneous, the classification reveals that they are precisely the Fisher information tensors, which constitute a higher-order generalization of the Fisher information matrix.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37580",
  "author_total": 2,
  "authors": [
    {
      "name": "Tian Gao"
    },
    {
      "name": "Dan Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eqbnm14jf23p7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37580",
  "fulltext_url": null,
  "id": "eqbnm14jf23p7",
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  "landing_url": "https://arxiv.org/abs/2609.37580",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "arxiv",
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      "openalex",
      "2604|Point processes and geometric inequalities"
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  "openalex": "W7214940637",
  "pdf_url": "https://arxiv.org/pdf/2609.37580",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eqbnm14jf23p7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37580",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37580"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
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    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
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  ],
  "title": "Tensor valuations on Sobolev spaces",
  "title_text": "Tensor valuations on Sobolev spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/eqbnm14jf23p7",
  "venue": "arXiv",
  "versions": []
}