{
  "abstract": "Let $g=w|dz|^2$ be an affine special Kähler metric on a punctured disc and let $Ξ=q(z)\\,dz^3$ be its associated holomorphic cubic differential. We prove that if the $g$-area of concentric punctured neighbourhoods grows at most polynomially, then $q$ is meromorphic at the puncture. More precisely, an area bound of order $\\eps^{-N}$ forces every pole of $q$ to have order strictly less than $N+3$. Hence an essential singularity of the cubic differential rules out every polynomial area upper bound. The proof associates to $(g,Ξ)$ a curvature $-1$ conformal pseudometric and applies the Ahlfors--Schwarz lemma, followed by the submean inequality for holomorphic functions. We also discuss the identically zero cubic differential and the borderline logarithmic growth responsible for the strict pole-order bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32087",
  "author_total": 3,
  "authors": [
    {
      "name": "Yiqian Shi"
    },
    {
      "name": "Ke Wang"
    },
    {
      "name": "Bin Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/56kfx0gf36rvg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32087",
  "fulltext_url": null,
  "id": "56kfx0gf36rvg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32087",
  "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",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7214748036",
  "pdf_url": "https://arxiv.org/pdf/2609.32087",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/56kfx0gf36rvg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32087",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32087"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Polynomial area growth for special Kähler metrics",
  "title_text": "Polynomial area growth for special Kähler metrics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/56kfx0gf36rvg",
  "venue": "arXiv",
  "versions": []
}