{"paper":{"title":"Normal curvature bounds along the mean curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Hong Huang","submitted_at":"2009-06-16T14:57:27Z","abstract_excerpt":"Let $(M^n,g_0)$ and $(\\bar{M}^{n+1},\\bar{g})$ be complete Riemannian manifolds with $|\\bar{\\nabla}^k\\bar{Rm}|\\le \\bar{C}$ for $k \\le 2$, and suppose there is an isometric immersion $F_0: M^n \\rightarrow \\bar{M}^{n+1}$ with bounded second fundamental form. Let $F_t: M^n \\rightarrow \\bar{M}^{n+1}$ ($t\\in [0,T]$) be a family of immersions evolving by mean curvature flow with initial data $F_0$ and with uniformly bounded second fundamental forms.\n  We show that the supremum and infimum of the normal curvature of the immersions $F_t$ vary at a bounded rate. This is an analogue of a result of Rong a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2889","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":""},"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"}