{
  "abstract": "We prove sharp two-eigenvalue isoperimetric inequalities for Neumann and Aharonov--Bohm Neumann spectra on surfaces. If $Ω\\subset\\mathbb S^2$ is smooth, simply connected and proper, then the harmonic mean of $μ_2(Ω)$ and $μ_3(Ω)$ is bounded above by the first positive Neumann eigenvalue of the equal-area geodesic disk, with equality only for disks. For simply connected surfaces with Gaussian curvature bounded above, we obtain the magnetic analogue for the first two Aharonov--Bohm eigenvalues. The proof combines a two-dimensional reciprocal Rayleigh--Ritz principle with Green-level comparison. A key additional ingredient is a spectral ordering theorem for magnetic spherical caps: for $0<ν<1/2$, the first two eigenvalues lie in the angular sectors of effective orders $ν$ and $1-ν$. We prove this by the factorization $L_0=T^*T$, $L_1=TT^*$ and an exact Neumann--Dirichlet spectral shift. We also obtain sharp full-sphere and closed-surface bounds, and an annular inequality in terms of conformal modulus and flux.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24488",
  "author_total": 2,
  "authors": [
    {
      "name": "Daguang Chen"
    },
    {
      "name": "Chengxi Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6nn9ncprb0sze.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24488",
  "fulltext_url": null,
  "id": "6nn9ncprb0sze",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24488",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7214037143",
  "pdf_url": "https://arxiv.org/pdf/2609.24488",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6nn9ncprb0sze.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24488",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24488"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Sharp harmonic-mean inequalities for Neumann and Aharonov--Bohm spectra",
  "title_text": "Sharp harmonic-mean inequalities for Neumann and Aharonov--Bohm spectra",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/6nn9ncprb0sze",
  "venue": "arXiv",
  "versions": []
}