{"paper":{"title":"Ancient solutions for Andrews' hypersurface flow","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jiuru Zhou, Peng Lu","submitted_at":"2018-12-12T13:07:58Z","abstract_excerpt":"We construct the ancient solutions of the hypersurface flows in Euclidean spaces studied by B. Andrews in 1994. As time $t \\rightarrow 0^-$ the solutions collapse to a round point where $0$ is the singular time. But as $t\\rightarrow-\\infty$ the solutions become more and more oval. Near the center the appropriately-rescaled pointed Cheeger-Gromov limits are round cylinder solutions $S^J \\times \\mathbb{R}^{n-J}$, $1 \\leq J \\leq n-1$. These results are the analog of the corresponding results in Ricci flow ($J=n-1$) and mean curvature flow."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04926","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"}