{"paper":{"title":"Mean curvature flow with generic low-entropy initial data","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Christos Mantoulidis, Felix Schulze, Kyeongsu Choi, Otis Chodosh","submitted_at":"2021-02-23T23:07:11Z","abstract_excerpt":"We prove that sufficiently low-entropy closed hypersurfaces can be perturbed so that their mean curvature flow encounters only spherical and cylindrical singularities. Our theorem applies to all closed surfaces in $\\mathbb{R}^3$ with entropy $\\leq 2$ and to all closed hypersurfaces in $\\mathbb{R}^4$ with entropy $\\leq \\lambda(\\mathbb{S}^1 \\times \\mathbb{R}^2)$. When combined with recent work of Daniels-Holgate, this strengthens Bernstein-Wang's low-entropy Schoenflies-type theorem by relaxing the entropy bound to $\\lambda(\\mathbb{S}^1 \\times \\mathbb{R}^2)$. Our techniques, based on a novel den"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.11978","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2102.11978/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}