{
  "abstract": "We prove that the Y-partition into three equal sectors is the minimal spectral three-partition both for the Dirichlet Laplacian on the unit disc and for the planar harmonic oscillator $-Δ+|x|^2$, with minimal energies $j_{3/2,1}^{2}$ and $5$; for the disc, this confirms a conjecture of Helffer and Hoffmann-Ostenhof. The minimizing regular strong partition is unique up to rotation, and every open minimizing partition has cells with the Dirichlet form domains of the sectors. The proof is a positive radial transplantation to the sphere that preserves segregation and matches the angular-energy measures of the separated model states; the three-lune theorem of Helffer, Hoffmann-Ostenhof, and Terracini then gives the lower bound. The transplantation lowers the shifted quadratic form by a nonnegative defect with strictly positive radial weight; in the equality case, spherical equipartition makes the defects vanish, which separates variables, and a Poincaré inequality on the circle identifies the sectors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21964",
  "author_total": 1,
  "authors": [
    {
      "name": "Mikael Sundqvist"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9p1ycqvf48xg1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21964",
  "fulltext_url": null,
  "id": "9p1ycqvf48xg1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21964",
  "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.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7213896103",
  "pdf_url": "https://arxiv.org/pdf/2609.21964",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9p1ycqvf48xg1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21964",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21964"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Y-partition is the optimal three-partition for the disc and the harmonic oscillator",
  "title_text": "The Y-partition is the optimal three-partition for the disc and the harmonic oscillator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/9p1ycqvf48xg1",
  "venue": "arXiv",
  "versions": []
}