{"paper":{"title":"A Komatu-Loewner Equation for Multiple Slits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Christoph B\\\"ohm, Wolfgang Lauf","submitted_at":"2014-05-10T19:32:19Z","abstract_excerpt":"We give a generalization of the Komatu-Loewner equation to multiple slits. Therefore, we consider an $n$-connected circular slit disk $\\Omega$ as our initial domain minus $m\\in \\mathbb{N}$ disjoint, simple and continuous curves that grow from the outer boundary $\\partial \\mathbb{D}$ of $\\Omega$ into the interior. Consequently we get a decreasing family $(\\Omega_t)_{t\\in[0,T]}$ of domains with $\\Omega_0=\\Omega$. We will prove that the corresponding Riemann mapping functions $g_t$ from $\\Omega_t$ onto a circular slit disk, which are normalized by $g_t(0)=0$ and $g_t'(0)>0$, satisfy a Loewner equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2463","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"}