{
  "abstract": "The main purpose of this paper is to address an open problem posed by Huang, Rasila, and Zhu in [Anal. Math. 48(2022), 1069-1080]. We first establish a sharp Lipschitz continuity result for locally univalent harmonic Bloch mappings with respect to the pseudo hyperbolic metric. This result is then applied to demonstrate that harmonic $(K,K_0)$-quasiregular Bloch type mappings are Lipschitz continuous under the same metric, where $K\\geq1$ and $K_{0}\\geq0$. Moreover, the estimates obtained are asymptotically sharp as $K \\to 1^+$ and $K_0 \\to 0^+$. In particular, when $K_0 = 0$, our theorem provides a solution to the aforementioned open problem in the asymptotically sharp sense.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33140",
  "author_total": 4,
  "authors": [
    {
      "name": "Shaolin Chen"
    },
    {
      "name": "Hidetaka Hamada"
    },
    {
      "name": "Manzi Huang"
    },
    {
      "name": "Lei Jin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/995bc0c0d66q9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33140",
  "fulltext_url": null,
  "id": "995bc0c0d66q9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33140",
  "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"
    ],
    [
      "openalex",
      "2608|Analytic and geometric function theory"
    ]
  ],
  "openalex": "W7214751796",
  "pdf_url": "https://arxiv.org/pdf/2609.33140",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/995bc0c0d66q9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33140",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33140"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The sharp Lipschitz continuity problem with respect to the pseudo hyperbolic metric",
  "title_text": "The sharp Lipschitz continuity problem with respect to the pseudo hyperbolic metric",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/995bc0c0d66q9",
  "venue": "arXiv",
  "versions": []
}