A gap theorem of self-shrinkers

2012/12/25 by Qing-Ming Cheng, Cheng, Qing-Ming, Guoxin Wei +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1212.6028

openalex publication_date 2012/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study complete self-shrinkers in Euclidean space and prove that an n-dimensional complete self-shrinker with polynomial volume growth in Euclidean space ℝⁿ⁺¹ is isometric to either ℝⁿ, Sⁿ(√(n)), or ℝ^n-m× S^m (√(m)), 1≤ m≤ n-1, if the squared norm S of the second fundamental form is constant and satisfies S

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