{
  "abstract": "We analyse the essential spectrum of ${\\mathcal M} = {\\operatorname{curl}} {\\operatorname{curl}}$ acting on divergence-free vector fields in unbounded domains of $\\mathbb{R}^3$. We show that $σ_e({\\mathcal M}) = [0,+\\infty)$ in quasi-conical domains and $σ_e({\\mathcal M}) \\neq \\emptyset$ in quasi-cylindrical domains. For horn-shaped domains with circular cross-section and eventually mean-convex boundary, we establish that $σ_e({\\mathcal M}) = \\emptyset$, independently of their volume. For horns with annular cross-section, the transverse normal harmonic field determines an effective one-dimensional Schrödinger operator $H_V$ with $σ_e({\\mathcal M}) \\supseteq σ_e(H_V)$. Finally, for a concrete family of perforated exponential horns with a double-exponential hole, we show that depending on the rate of shrinking of the hole at infinity, either $σ_e({\\mathcal M}) = \\emptyset$, or $σ_e({\\mathcal M}) = [γ^2, +\\infty)$, or $σ_e({\\mathcal M}) = [0,+\\infty)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20339",
  "author_total": 2,
  "authors": [
    {
      "name": "Francesco Ferraresso"
    },
    {
      "name": "Marco Marletta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bmnp09gwbv2bn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20339",
  "fulltext_url": null,
  "id": "bmnp09gwbv2bn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20339",
  "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"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7213609264",
  "pdf_url": "https://arxiv.org/pdf/2609.20339",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bmnp09gwbv2bn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20339",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20339"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Essential spectral geometry of the Maxwell system in unbounded domains",
  "title_text": "Essential spectral geometry of the Maxwell system in unbounded domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/bmnp09gwbv2bn",
  "venue": "arXiv",
  "versions": []
}