{"paper":{"title":"Guiding Isotopies and Holomorphic Motions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Frederick. P. Gardiner, Yunping Jiang","submitted_at":"2013-04-28T19:15:03Z","abstract_excerpt":"We develop an isotopy principle for holomorphic motions. Our main result concerns the extendability of a holomorphic motion of a finite subset $E$ of a Riemann surface $Y$ parameterized by a point $t$ in a pointed hyperbolic surface $(X, t_{0})$. If a holomorphic motion from $E$ to $E_{t}$ in $Y$ has a guiding quasiconformal isotopy, then there is a holomorphic extension to any new point $p$ in $Y-E$ that follows the guiding isotopy. The proof gives a canonical way to replace a quasiconformal motion of the $(n+1)^{th}$ point by a holomorphic motion while leaving unchanged the given holomorphic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7502","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"}