{"paper":{"title":"Rogosinski's lemma for univalent functions, hyperbolic Archimedean spirals and the Loewner equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Oliver Roth, Sebastian Schlei{\\ss}inger","submitted_at":"2013-11-04T12:34:43Z","abstract_excerpt":"We describe the region $\\mathcal{V}(z_0)$ of values of $f(z_0)$ for all normalized bounded univalent functions $f$ in the unit disk $\\mathbb{D}$ at a fixed point $z_0 \\in \\mathbb{D}$. The proof is based on identifying $\\mathcal{V}(z_0)$ as the reachable set of the radial Loewner differential equation. We also prove an analogous result for the upper half-plane using the chordal Loewner equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0677","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"}