{
  "abstract": "We prove an interior Lipschitz estimate with a sharp height threshold for continuous viscosity solutions of the three-dimensional special Lagrangian equation with subcritical phase $|Θ|<π/2$. If \\[ osc_{B_R}u\\leq MR^2,\\qquad 0\\leq M<\\secΘ, \\] then $Lip_{B_{ρR}}u\\leq CR$ for some $ρ>0$ and $C>0$ depending only on $|Θ|$ and $M$. The threshold is optimal: at $M=\\secΘ$, there are entire real-analytic solutions whose Lipschitz seminorms are unbounded on every fixed interior ball. The proof uses a two-point maximum principle and algebraic identities specific to dimension three.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01986",
  "author_total": 2,
  "authors": [
    {
      "name": "Caiyan Li"
    },
    {
      "name": "Wei Wei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ff12c3svd8vvy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01986",
  "fulltext_url": null,
  "id": "ff12c3svd8vvy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01986",
  "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"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7216378723",
  "pdf_url": "https://arxiv.org/pdf/2610.01986",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ff12c3svd8vvy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01986",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01986"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp Small-Height Estimates for Subcritical Special Lagrangian Equations in Dimension Three",
  "title_text": "Sharp Small-Height Estimates for Subcritical Special Lagrangian Equations in Dimension Three",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/ff12c3svd8vvy",
  "venue": "arXiv",
  "versions": []
}