A gap Theorem on closed self-shrinkers of mean curvature flow

2025/03/01 by Zhao, Yuhang · 1 citation
#53C20 #53C24 #53C42 #53E10 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.00505

Abstract

In this paper, we prove a pinching theorem for n-dimensional closed self-shrinkers of the mean curvature flow. If the squared norm of the second fundamental form of a closed self-shrinker of arbitrary codimension satisfies: | \uppercase\expandafter\romannumeral2 |² ≤ 1 +(1)/(10 π(n+2)), then it must be the standard sphere Sⁿ(√(n)). This result may provide some evidence for the open problem 13.76 in \citeandrews2022extrinsic.

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• The Rigidity Theorems for Self-Shrinkers in the Mean Curvature Flow

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