{"paper":{"title":"Remarks on Loewner Chains Driven by Finite Variation Functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Atul Shekhar, Huy Tran, Yilin Wang","submitted_at":"2017-10-19T18:06:24Z","abstract_excerpt":"To explore the relation between properties of Loewner chains and properties of their driving functions, we study Loewner chains driven by functions $U$ of finite total variation. Under some appropriate conditions, we show existence of the simple trace $\\gamma$ and establish continuity of the map $U$ to $\\gamma$ with respect to uniform topology on $\\gamma$ and the total variation topology on $U$. In the spirit of work of Wong and Tran-Lind, we also obtain conditions on the driving function that ensures the trace to be continuously differentiable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07302","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"}