{
  "abstract": "In this paper, we prove the strict Faber-Krahn inequality for non-negative-mass Dirac operators on simply connected domains with infinite-mass boundary condition. Denoting the first positive eigenvalue of the corresponding Dirac operator with mass $m\\geq 0$ as $λ_1^{+}(Ω;m)$, our main result shows that \\begin{equation*} λ_1^{+}(Ω;m)\\geq λ_1^{+}(B_{|Ω|};m), \\end{equation*} where $B_{|Ω|}$ is the disk with the same area as the domain $Ω$, and the equality is strictly valid if and only if $Ω=B_{|Ω|}$. The key observation leading to the proof is that the upper component of the Dirac spinor associated with $λ_1^{+}(Ω;m)$ is non-vanishing over $Ω$, which is proved by exploiting its Dirac current and the associated stream function. Based on this global non-vanishing property, we construct a sphere-valued spinor map of degree one, which allows a sharp comparison with the radial disk profile using the planar isoperimetry.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08665",
  "author_total": 2,
  "authors": [
    {
      "name": "Habib Ammari"
    },
    {
      "name": "Jiayu Qiu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dfaq26prv4c5g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08665",
  "fulltext_url": null,
  "id": "dfaq26prv4c5g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08665",
  "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": "W7221017606",
  "pdf_url": "https://arxiv.org/pdf/2610.08665",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dfaq26prv4c5g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08665",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08665"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On the Dirac Faber-Krahn Conjecture",
  "title_text": "On the Dirac Faber-Krahn Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/dfaq26prv4c5g",
  "venue": "arXiv",
  "versions": []
}