{"paper":{"title":"Weak chord-arc curves and double-dome quasisymmetric spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Vyron Vellis","submitted_at":"2014-12-16T18:22:31Z","abstract_excerpt":"Let $\\Omega$ be a planar Jordan domain and $\\alpha>0$. We consider double-dome-like surfaces $\\Sigma(\\Omega,t^{\\alpha})$ over $\\overline{\\Omega}$ where the height of the surface over any point $x\\in\\overline{\\Omega}$ equals $\\text{dist}(x,\\partial\\Omega)^{\\alpha}$. We identify the necessary and sufficient conditions in terms of $\\Omega$ and $\\alpha$ so that these surfaces are quasisymmetric to $\\mathbb{S}^2$ and we show that $\\Sigma(\\Omega,t^{\\alpha})$ is quasisymmetric to the unit sphere $\\mathbb{S}^2$ if and only if it is linearly locally connected and Ahlfors $2$-regular."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5110","kind":"arxiv","version":1},"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"}