The second gap on complete self-shrinkers

2021/04/29 by Cheng, Qing-Ming, Wei, Guoxin, Yano, Wataru · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.14059

Abstract

In this paper, we study complete self-shrinkers in Euclidean space and prove that an n-dimensional complete self-shrinker in Euclidean space ℝⁿ⁺¹ is isometric to either ℝⁿ, Sⁿ(√(n)), or S^k (√(k))×ℝ^n-k, 1≤ k≤ n-1, if the squared norm S of the second fundamental form, f₃ are constant and S satisfies S<1.83379. We should remark that the condition of polynomial volume growth is not assumed.

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