{"paper":{"title":"Distortions of the Helicoid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Christine Breiner, Jacob Bernstein","submitted_at":"2008-05-30T14:35:34Z","abstract_excerpt":"Colding and Minicozzi have shown that an embedded minimal disk $0\\in\\Sigma\\subset B_R$ in $\\Real^3$ with large curvature at 0 looks like a helicoid on the scale of $R$. Near 0, this can be sharpened: on the scale of $|A|^{-1}(0)$, $\\Sigma$ is close, in a Lipschitz sense, to a piece of a helicoid. We use surfaces constructed by Colding and Minicozzi to see this description cannot hold on the scale $R$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.4775","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"}