{
  "abstract": "We study global and variational properties of $\\mathbb R$-equivariant minimal Lagrangian surfaces in the complex quadric $Q_2$ and the complex hyperbolic quadric $Q_2^*$ arising from loop group potentials. In the $Q_2^*$ case, we work under the timelike-axis condition throughout the associated $\\mathbb{S}^1$-family. Excluding the flat case in $Q_2$, we give a necessary and sufficient criterion for closing in the $y$-direction: a member $f^{λ_0}$ closes if and only if the spectral ratio $μ_2/μ_1$ is a positive rational number. The closing parameters form a dense countable subset of $\\mathbb{S}^1$, while the non-closing parameters are dense and have full arc-length measure. The closing members yield cylindrical quotients in $Q_2$ and annular quotients in $Q_2^*$. Apart from the flat case in $Q_2$, the surfaces under consideration have infinite absolute total curvature. The equivariant surfaces considered here in $Q_2$ are unstable, whereas minimal Lagrangian surfaces in $Q_2^*$ are stable. Finally, for compact cylindrical domains of the $y$-closing surfaces in $Q_2$, we obtain explicit sufficient width conditions for Hamiltonian stability and instability under variations fixed near the boundary. We also establish the existence of a finite geometric critical width and determine it explicitly in the flat case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09555",
  "author_total": 1,
  "authors": [
    {
      "name": "Sihao Zeng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/110bd7gmzw621.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09555",
  "fulltext_url": null,
  "id": "110bd7gmzw621",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09555",
  "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"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7220974419",
  "pdf_url": "https://arxiv.org/pdf/2610.09555",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/110bd7gmzw621.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09555",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09555"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "$\\mathbb{R}$-equivariant minimal Lagrangian surfaces in the complex quadric $Q_{2}$ and the complex hyperbolic quadric $Q_{2}^{*}$",
  "title_text": "ℝ-equivariant minimal Lagrangian surfaces in the complex quadric Q_2 and the complex hyperbolic quadric Q_2^*",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/110bd7gmzw621",
  "venue": "arXiv",
  "versions": []
}