{"paper":{"title":"Quasiconformal Homogeneity of Genus Zero Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ferry Kwakkel, Vlad Markovic","submitted_at":"2009-10-06T16:29:24Z","abstract_excerpt":"A Riemann surface $M$ is said to be $K$-quasiconformally homogeneous if for every two points $p,q \\in M$, there exists a $K$-quasiconformal homeomorphism $f \\colon M \\rightarrow M$ such that $f(p) = q$. In this paper, we show there exists a universal constant $K_0 > 1$ such that if $M$ is a $K$-quasiconformally homogeneous hyperbolic genus zero surface other than the disk $\\mathbb{D}$, then $K \\geq K_0$. This answers a question by Gehring and Palka."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1050","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}