{
  "abstract": "Motivated by lower bound estimates of Payne and Escobar for the classical Steklov problem, we study sharp lower bounds for the first eigenvalue of Steklov-type problems on compact surfaces with smooth boundary. We prove that, if the Gaussian curvature satisfies K ≥ − α $K \\ge -\\alpha $ and the geodesic curvature of the boundary satisfies k g ≥ c > 0 $k_{g} \\ge c > 0$ , then the first eigenvalue of the Steklov-type eigenvalue problem satisfies an optimal inequality and equality holds only for the Euclidean disk. In particular, we obtain a sharp lower bound for the first eigenvalue of a Schrödinger-Steklov eigenvalue problem. If the Gaussian curvature satisfies K ≥ − α $K \\ge -\\alpha $ and the geodesic curvature satisfies k g ≥ c > 0 $k_{g} \\ge c > 0$ , then the first eigenvalue σ 1 $\\sigma _{1}$ satisfies σ 1 + α σ 1 ≥ c , $$ \\sigma _{1} + \\frac{\\alpha}{\\sigma _{1}} \\ge c, $$ where equality holds if and only if the surface is a Euclidean disk of radius 1 / c $1/c$ and α = 0 $\\alpha = 0$ . We also prove that the first eigenvalue of a fourth-order Steklov-type problem is bounded below by 2c under nonnegative Gaussian curvature, with equality again characterizing the Euclidean disk.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, Texas State University",
    "Department of Mathematics and Research Institute of Natural Sciences, Sookmyung Women’s University"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Gunhee Cho"
    },
    {
      "affs": [
        1
      ],
      "name": "Keomkyo Seo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3g35s2yet709c.bib",
  "cited_by": 0,
  "doi": "10.1186/s13661-026-02331-8",
  "fulltext_url": "https://doi.org/10.1186/s13661-026-02331-8",
  "id": "3g35s2yet709c",
  "issns": [
    "1687-2770",
    "1687-2762"
  ],
  "landing_url": "https://doi.org/10.1186/s13661-026-02331-8",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "QA299.6-433"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
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  "openalex": "W4411874049",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-01",
  "publisher": "SpringerOpen",
  "ris": "https://research.draconitic.com/paper/3g35s2yet709c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:46:14Z",
      "native_id": "f6d1dd951cef4c47a1e9b9a93b884f46",
      "source": "doaj",
      "url": "https://doi.org/10.1186/s13661-026-02331-8"
    }
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Spectral Theory in Mathematical Physics",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Sharp lower bounds for the first eigenvalue of Steklov-type eigenvalue problems on a compact surface",
  "title_text": "Sharp lower bounds for the first eigenvalue of Steklov-type eigenvalue problems on a compact surface",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T13:46:14Z",
  "url": "https://research.draconitic.com/paper/3g35s2yet709c",
  "venue": "Boundary Value Problems",
  "versions": []
}