Quadratically pinched submanifolds of the sphere via mean curvature flow with surgery

2021/09/08 by Mat Langford, Langford, Mat, Stephen Lynch +2
Mathematics · Physics and Astronomy · #53E10 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2109.03651

openalex publication_date 2021/09/08 · openalex created_date 2021/09/13 · openalex updated_date 2026/07/28

Abstract

We study mean curvature flow of n-dimensional submanifolds of S_K^n+ℓ, the round (n+ℓ)-sphere of sectional curvature K>0, under the quadratic curvature pinching condition |A|² < (1)/(n-2)|H|² + 4K when n≥ 8, |A|² < (4)/(3n)|H|²+(n)/(2)K when n=7, and |A|²

Citations

• An intrinsic rigidity theorem for minimal submanifolds in a sphere
• Minimal Varieties in Riemannian Manifolds

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