{"paper":{"title":"Radial extension of a bi-Lipschitz parametrization of a starlike Jordan curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"David Kalaj","submitted_at":"2010-11-23T19:50:46Z","abstract_excerpt":"In this paper we discus the radial extension $w$ of a bi-Lipschitz parameterization $F(e^{it})=f(t)$ of a starlike Jordan curve $\\gamma$ w.r. to 0. We show that, if parameterization is bi-Lipschitz, then the extension is bi-Lipschitz and consequently quasiconformal. If $\\gamma$ is the unit circle, then $\\mathrm{Lip}(f)=\\mathrm{Lip}(F)=\\mathrm{Lip}(w)=K_w$. If $\\gamma$ is not a circle centered at origin, and $F$ is a polar parametrization of $\\gamma$, then we show that $\\mathrm{Lip}(f)=\\mathrm{Lip}(F)<\\mathrm{Lip}(w)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5204","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"}