{"paper":{"title":"Quasiconformal extension of strongly spirallike functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Toshiyuki Sugawa","submitted_at":"2011-01-20T07:11:16Z","abstract_excerpt":"We show that a strongly $\\lambda$-spirallike function of order $\\alpha$ can be extended to a $\\sin(\\pi\\alpha/2)$-quasiconformal automorphism of the complex plane for $-\\pi/2<\\lambda<\\pi/2$ and $0<\\alpha<1$ with $|\\lambda|<\\pi\\alpha/2.$ In order to prove it, we provide several geometric characterizations of a strongly $\\lambda$-spirallike domain of order $\\alpha.$ We also give a concrete form of the mapping function of the standard strongly $\\lambda$-spirallike domain $U_{\\lambda,\\alpha}$ of order $\\alpha.$ A key tool of the present study is the notion of $\\lambda$-argument, which was developed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3831","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"}