Sharp pinching estimates for mean curvature flow in the sphere

2020/09/01 by Mat Langford, Langford, Mat, Huy The Nguyen +1
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2009.00986

Abstract

We prove a suite of asymptotically sharp quadratic curvature pinching estimates for mean curvature flow in the sphere which generalize Simons' rigidity theorem for minimal hypersurfaces. We then obtain derivative estimates for the second fundamental form which we utilize, via a compactness argument, to obtain a convexity estimate. Together, the convexity and cylindrical estimates yield a partial classification of singularity models. We also obtain new rigidity results for ancient solutions.

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