{"paper":{"title":"Singularity models of pinched solutions of mean curvature flow in higher codimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Keaton Naff","submitted_at":"2019-10-09T13:12:49Z","abstract_excerpt":"We consider ancient solutions to the mean curvature flow in $\\mathbb{R}^{n+1}$ ($n \\geq 3$) that are weakly convex, uniformly two-convex, and satisfy derivative estimates $|\\nabla A| \\leq \\gamma_1 |H|^2, |\\nabla^2 A| \\leq \\gamma_2 |H|^3$. We show that such solutions are noncollapsed. As an application, in arbitrary codimension, we consider compact $n$-dimensional ($n \\geq 5$) solutions to the mean curvature flow in $\\mathbb{R}^N$ that satisfy the pinching condition $|H| > 0$ and $|A|^2 < c(n) |H|^2$, $c(n) = \\min\\{\\frac{1}{n-2}, \\frac{3(n+1)}{2n(n+2)}\\}$. We conclude that any blow-up model at "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.03968","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1910.03968/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"}