Classification and rigidity of self-shrinkers in the Mean curvature flow

2012/01/23 by Haizhong Li, Yong Wei, Li, Haizhong +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1201.4623

openalex publication_date 2012/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we first use the method of Colding and Minicozzi [5] to show that K. Smoczyk's classification theorem [16] for complete self-shrinkers in higher codimension also holds under a weaker condition. Then as an application, we give some rigidity results for self-shrinkers in arbitrary codimension.

Citations

• On Chernʼs problem for rigidity of minimal hypersurfaces in the spheres
• Curvature estimates for minimal hypersurfaces
• Minimal Varieties in Riemannian Manifolds
• Generic mean curvature flow I; generic singularities

Related

• Complete self-shrinkers of the mean curvature flow
• A Gap Theorem for Self-shrinkers of the Mean Curvature Flow in Arbitrary Codimension
• F-stability for self-shrinking solutions to mean curvature flow
• The Stability of Self-Shrinkers of Mean Curvature Flow in Higher Codimension
• A maximum principle for self-shrinkers and some consequences