{"paper":{"title":"Quasiconformal non-parametrizability of almost smooth spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Pekka Pankka, Vyron Vellis","submitted_at":"2015-05-20T09:13:02Z","abstract_excerpt":"We show that, for each $n\\ge 3$, there exists a smooth Riemannian metric $g$ on a punctured sphere $\\mathbb{S}^n\\setminus \\{x_0\\}$ for which the associated length metric extends to a length metric $d$ of $\\mathbb{S}^n$ with the following properties: the metric sphere $(\\mathbb{S}^n,d)$ is Ahlfors $n$-regular and linearly locally contractible but there is no quasiconformal homeomorphism between $(\\mathbb{S}^n,d)$ and the standard Euclidean sphere $\\mathbb{S}^n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05293","kind":"arxiv","version":2},"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"}