{
  "abstract": "In this paper, we study the first variational Steklov eigenvalue of the $ p$-Laplace equation on exterior domain $ Ω^{\\text{ext}}$ for $ 1< p <n$. If $ Ω$ is convex and $ \\partial Ω\\in C^{1,1}$, we prove a sharp lower bound in terms of $p$-logarithmic mean of the principal curvatures of $ \\partial Ω$. For the linear case $ p=2$, our estimate reduces to the logarithmic mean bound of Bundrock et al. (arXiv:2511.09490). We also derive an upper bound in terms of a boundary isocapacitary constant. The analysis relies on the established finite energy theory on exterior domains, together with a decay estimate for $p$-harmonic extensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11517",
  "author_total": 2,
  "authors": [
    {
      "name": "Yating Niu"
    },
    {
      "name": "Tao Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6m8ktdh5edcdd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11517",
  "fulltext_url": null,
  "id": "6m8ktdh5edcdd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11517",
  "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.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7212240391",
  "pdf_url": "https://arxiv.org/pdf/2609.11517",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6m8ktdh5edcdd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11517",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11517"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A sharp curvature lower bound for the first exterior p-harmonic Steklov eigenvalue",
  "title_text": "A sharp curvature lower bound for the first exterior p-harmonic Steklov eigenvalue",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/6m8ktdh5edcdd",
  "venue": "arXiv",
  "versions": []
}