{"paper":{"title":"Curves in Banach spaces which allow a $C^2$ parametrization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CA","authors_text":"Jakub Duda, Ludek Zajicek","submitted_at":"2006-03-31T09:19:37Z","abstract_excerpt":"We give a complete characterization of those $f: [0,1] \\to X$ (where $X$ is a Banach space which admits an equivalent Fr\\'echet smooth norm) which allow an equivalent $C^2$ parametrization. For $X=\\R$, a characterization is well-known. However, even in the case $X=\\R^2$, several quite new ideas are needed. Moreover, the very close case of parametrizations with a bounded second derivative is solved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603735","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"}