{"paper":{"title":"Parametric representation of univalent functions with boundary regular fixed points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Pavel Gumenyuk","submitted_at":"2016-03-13T16:03:33Z","abstract_excerpt":"Given a set $\\mathfrak S$ of conformal maps of the unit disk $\\mathbb D$ into itself that is closed under composition, we address the question whether $\\mathfrak S$ can be represented as the reachable set of a Loewner - Kufarev - type ODE $\\mathrm{d}w_t/\\mathrm{d}t=G_t\\circ w_t$, $w_0=\\mathsf{id}_{\\mathbb D}$, where the control functions $t\\mapsto G_t$ form a convex cone $\\mathcal M_{\\mathfrak S}$. For the set of all conformal $\\varphi:\\mathbb D\\to\\mathbb D$ with $\\varphi(0)=0$, $\\varphi'(0)>0$, an affirmative answer to this question is the essence of Loewner's well-known Parametric Representa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04043","kind":"arxiv","version":4},"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"}