{
  "abstract": "In this paper, we prove that for two cyclically ordered sequences of complex numbers of unit modulus $(ξ_j)_{j=1}^{n}$ and $(ζ_j)_{j=1}^{n}$ the inequality: $$\\bigg|\\sum_{m=1}^{n}(ξ_{m+1}-ξ_m)ζ_m\\bigg|^2+ \\bigg|\\sum_{m=1}^{n}(ξ_{m+1}-ξ_m)ζ_m^{-1}\\bigg|^2\\leqslant 4n^2\\sin^2\\fracπ{n}$$ holds for $n\\geqslant 4$. As a consequence, for $n=4,$ we disprove Hall's conjecture on Heinz type inequality for harmonic self-mappings of the unit disk. The connection with the theory of elliptic billiards via the Mather beta function will also be given.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07864",
  "author_total": 2,
  "authors": [
    {
      "name": "Vladimir Božin"
    },
    {
      "name": "Petar Melentijević"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/95cdsvhqvz8t9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07864",
  "fulltext_url": null,
  "id": "95cdsvhqvz8t9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07864",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "openalex",
      "2608|Analytic and geometric function theory"
    ]
  ],
  "openalex": "W7212008289",
  "pdf_url": "https://arxiv.org/pdf/2609.07864",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/95cdsvhqvz8t9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07864",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07864"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Reverse Heinz type inequality, Mather beta function and coefficient estimates",
  "title_text": "Reverse Heinz type inequality, Mather beta function and coefficient estimates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/95cdsvhqvz8t9",
  "venue": "arXiv",
  "versions": []
}