{"paper":{"title":"Quasisymmetric spheres over Jordan domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Jang-Mei Wu, Vyron Vellis","submitted_at":"2014-07-18T15:10:46Z","abstract_excerpt":"Let $\\Omega$ be a planar Jordan domain. We consider double-dome-like surfaces $\\Sigma$ defined by graphs of functions of $dist( \\cdot ,\\partial \\Omega)$ over $\\Omega$. The goal is to find the right conditions on the geometry of the base $\\Omega$ and the growth of the height so that $\\Sigma$ is a quasisphere, or quasisymmetric to $\\mathbb{S}^2$. An internal uniform chord-arc condition on the constant distance sets to $\\partial \\Omega$, coupled with a mild growth condition on the height, gives a close-to-sharp answer. Our method also produces new examples of quasispheres in $\\mathbb{R}^n$, for a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5029","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"}