{
  "abstract": "In 2012, Iwaniec, Kovalev and Onninen proposed an upper Nitsche--Grötzsch type estimate for harmonic $K$-quasiconformal homeomorphisms between circular annuli: in normalized form, every such map $h:A(1,s)\\to A(1,S)$ should satisfy \\[ S \\leq \\frac{K+1}{2}s-\\frac{K-1}{2s}. \\] The radial and spiral-radial one-mode models explain why this estimate is natural. We show that this one-mode evidence does not extend to the unrestricted non-radial class. For every $1<s<S$, we construct a non-radial harmonic orientation-preserving diffeomorphism $h:A(1,s)\\to A(1,S)$ with \\[ \\norm{ω_h}_{\\infty}<\\frac{S-s}{S-s^{-1}}, \\] strictly below the conjectural threshold. Thus, the dilatation lower bound predicted by the conjecture fails, even for smooth harmonic diffeomorphisms with prescribed circular boundary components. The construction uses a small high-frequency reparametrization of the outer boundary: it lowers the first Fourier-mode dilatation by order $t^2$, while the compensating high modes are exponentially damped at the inner boundary. We also record structured regimes in which the one-mode estimate survives, including an inner-boundary anti-conformal energy condition, a Fourier leakage criterion, and a low-frequency spectral stability result. In the minimal-surface interpretation, the upper radial model is helicoidal and vertical-periodic rather than single-valued catenoidal; accordingly, the counterexamples give vertical-periodic minimal annuli with slope below the expected helicoidal threshold, and lead to a non-radial extremal problem for harmonic annulus diffeomorphisms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29795",
  "author_total": 3,
  "authors": [
    {
      "name": "David Kalaj"
    },
    {
      "name": "Jinsong Liu"
    },
    {
      "name": "Jian-feng Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/be03pmqyt19e2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29795",
  "fulltext_url": null,
  "id": "be03pmqyt19e2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29795",
  "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.CV"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Analytic and geometric function theory"
    ]
  ],
  "openalex": "W7214382402",
  "pdf_url": "https://arxiv.org/pdf/2609.29795",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/be03pmqyt19e2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29795",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29795"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On an Iwaniec--Kovalev--Onninen Conjecture for harmonic quasiconformal annulus mappings",
  "title_text": "On an Iwaniec--Kovalev--Onninen Conjecture for harmonic quasiconformal annulus mappings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/be03pmqyt19e2",
  "venue": "arXiv",
  "versions": []
}