{
  "abstract": "A self-homeomorphism $h$ of the unit circle $\\mathbb{T}$ is strongly symmetric if it is absolutely continuous and $\\log h'\\in\\text{VMO}(\\mathbb{T})$. Let $P_h^-$ be the anti-analytic component of the pullback operator $P_h: F\\mapsto F\\circ h$ on $\\text{BMOA}(\\mathbb{D})$, where $\\mathbb{D}$ is the unit disk. P. Jones proved $P_h$ is bounded on BMO if and only if $h$ is strongly quasisymmetric. Fan, Hu, and Shen showed that the strong symmetry of $h$ yields the compactness of $P_h^-$, and raised the question of whether the converse is true. We answer this question affirmatively, establishing that $P_h^-$ is compact if and only if $\\log h'\\in\\text{VMO}(\\mathbb{T}))$, which completes the VMO theory of the universal Teichmüller space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28074",
  "author_total": 2,
  "authors": [
    {
      "name": "Liu Tailiang"
    },
    {
      "name": "Shen Yuliang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/91jyt991ad55n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28074",
  "fulltext_url": null,
  "id": "91jyt991ad55n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28074",
  "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": "W7204763318",
  "pdf_url": "https://arxiv.org/pdf/2608.28074",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/91jyt991ad55n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2608.28074",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28074"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Compactness Characterization of Strongly Symmetric Homeomorphisms",
  "title_text": "A Compactness Characterization of Strongly Symmetric Homeomorphisms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/91jyt991ad55n",
  "venue": "arXiv",
  "versions": []
}