{"paper":{"title":"An improved bound for Sullivan's convex hull theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Andrew Yarmola, Martin Bridgeman, Richard Canary","submitted_at":"2014-07-14T22:31:54Z","abstract_excerpt":"Sullivan showed that there exists $K_0$ such that if $\\Omega\\subset \\hat{\\mathbb{C}}$ is a simply connected hyperbolic domain, then there exists a conformally natural $K_0$-quasiconformal map from $\\Omega$ to the boundary ${\\rm Dome}(\\Omega)$ of the convex hull of its complement which extends to the identity on $\\partial\\Omega$. Explicit upper and lower bounds on $K_0$ were obtained by Epstein, Marden, Markovic and Bishop. We improve on these bounds, by showing that one may choose $K_0\\le 7.1695$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3838","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"}