{
  "abstract": "Let $\\text{HQS}(\\mathbb{R})$ denote the class of increasing homeomorphisms of the real line $\\mathbb{R}$ that admit harmonic quasiconformal extensions to the upper half-plane $\\mathbb{H}$. Kalaj and Pavlović proved that a homeomorphism $h$ belongs to $\\text{HQS}(\\mathbb{R})$ if and only if $h$ is bi-Lipschitz and the Hilbert transform of $h'$ belongs to $L^\\infty(\\mathbb{R})$, and asked whether $\\text{HQS}(\\mathbb{R})$ is a group under composition. We give a negative answer to this question. Further, we show that the Beltrami coefficients of harmonic quasiconformal mappings of $\\mathbb{H}$ can be identified with the open unit ball of $H^\\infty(\\mathbb{H})$. Finally, we study the topology of $\\text{HQS}(\\mathbb{R})$ and prove that it is contractible in the topology inherited from the BMO-Teichmüller space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00860",
  "author_total": 2,
  "authors": [
    {
      "name": "Liu Tailiang"
    },
    {
      "name": "Shen Yuliang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1nv6xypwym7rv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00860",
  "fulltext_url": null,
  "id": "1nv6xypwym7rv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00860",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00860",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1nv6xypwym7rv.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00860",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00860"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Harmonic Quasiconformal Mappings in the BMO-Teichmüller space",
  "title_text": "Harmonic Quasiconformal Mappings in the BMO-Teichmüller space",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/1nv6xypwym7rv",
  "venue": "arXiv",
  "versions": []
}