{
  "abstract": "A generalization of the classical Gage's upper bound for the fundamental tone of the Laplacian on complete non-compact Riemannian manifolds to the $p$-Laplacian context is obtained. As an application, upper estimates for the $p$-fundamental tone of complete non-compact submanifolds of space forms with constant nonpositive sectional curvature, and for a class of product spaces, are presented.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21877",
  "author_total": 2,
  "authors": [
    {
      "name": "Matheus Nunes Soares"
    },
    {
      "name": "Fábio reis dos Santos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b580kkmnqks7a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21877",
  "fulltext_url": null,
  "id": "b580kkmnqks7a",
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  "landing_url": "https://arxiv.org/abs/2609.21877",
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
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      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
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  "openalex": "W7213890147",
  "pdf_url": "https://arxiv.org/pdf/2609.21877",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b580kkmnqks7a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21877",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21877"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Gage-type estimate for the $p$-fundamental tone and applications to submanifolds",
  "title_text": "A Gage-type estimate for the p-fundamental tone and applications to submanifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/b580kkmnqks7a",
  "venue": "arXiv",
  "versions": []
}