{"paper":{"title":"The Loewner Equation for Multiple Slits, Multiply Connected Domains and Branch Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Christoph B\\\"ohm, Sebastian Schlei{\\ss}inger","submitted_at":"2014-10-07T17:59:24Z","abstract_excerpt":"Let $\\gamma_1,\\gamma_2:[0,T]\\to \\overline{\\mathbb{D}}\\setminus\\{0\\}$ be parametrizations of two slits $\\Gamma_1:=\\gamma(0,T], \\Gamma_2=\\gamma_2(0,T]$ such that $\\Gamma_1$ and $\\Gamma_2$ are disjoint. \\\\ Let $g_t$ to be the unique normalized conformal mapping from $\\mathbb{D}\\setminus (\\gamma_1[0,t]\\cup \\gamma_2[0,t])$ onto $\\mathbb{D}$ with $g_t(0)=0,$ $g'_t(0)>0$. Furthermore, for $k=1,2$, denote by $h_{k;t}$ the unique normalized conformal mapping from $\\mathbb{D}\\setminus \\gamma_k[0,t]$ onto $\\mathbb{D}$ with $h_{k;t}(0)=0,$ ${h'_{k;t}(0)}>0$.\\\\ Loewner's famous theorem (\\cite{Loewner:1923}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1825","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"}