{"paper":{"title":"Uniformization of Sierpi\\'nski carpets in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Mario Bonk","submitted_at":"2010-09-21T13:50:18Z","abstract_excerpt":"Let $S_i$, $i\\in I$, be a countable collection of Jordan curves in the extended complex plane $\\Sph$ that bound pairwise disjoint closed Jordan regions. If the Jordan curves are uniform quasicircles and are uniformly relatively separated, then there exists a quasiconformal map $f\\: \\Sph\\ra \\Sph$ such that $f(S_i)$ is a round circle for all $i\\in I$. This implies that every Sierpi\\'nski carpet in $\\oC$ whose peripheral circles are uniformly relatively separated uniform quasicircles can be mapped to a round Sierpi\\'nski carpet by a quasisymmetric map."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4094","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"}