Quantitative long range curvature estimate for mean curvature flow

2021/08/26 by Jingze Zhu, Zhu, Jingze
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2108.11852

openalex publication_date 2021/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that smooth convex α-noncollapsed ancient mean curvature flow satisfies a quantitative curvature estimate H(y,t)≤ CH(x,t)(H(x,t)|x-y|+1)² for any pair of x,y. In other words, the rescaled curvature grows at most quadratically in terms of the rescaled extrinsic distance.

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