{
  "abstract": "We study the Steklov problem on non-compact exterior free-boundary minimal surfaces. Boundary values need not determine a unique harmonic extension, so the operator also requires a prescription at infinity. For proper surfaces in $\\mathbb{R}^3$ with compact boundary and finitely many regular ends of finite total curvature, we construct a natural class of such prescriptions. Every resulting operator is self-adjoint with compact resolvent; consequently, its spectrum is discrete, bounded below, and tends to $+\\infty$. If the coordinate functions have linearly independent boundary traces, the prescription can be chosen so that these traces are eigenfunctions with eigenvalue $-1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29318",
  "author_total": 1,
  "authors": [
    {
      "name": "Igor Kozyrev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a7rspngx6rn03.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29318",
  "fulltext_url": null,
  "id": "a7rspngx6rn03",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29318",
  "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.DG"
    ],
    [
      "arxiv",
      "math.SP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.29318",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a7rspngx6rn03.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29318",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29318"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Discreteness of the Steklov Spectrum for Exterior Non-Compact Free-Boundary Minimal Surfaces with Regular Ends of Finite Total Curvature",
  "title_text": "Discreteness of the Steklov Spectrum for Exterior Non-Compact Free-Boundary Minimal Surfaces with Regular Ends of Finite Total Curvature",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/a7rspngx6rn03",
  "venue": "arXiv",
  "versions": []
}