The Rigidity Theorems of Self Shrinkers via Gauss maps

2012/03/06 by Qi Ding, Y. L. Xin, Ding, Qi +3
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1203.1096

openalex publication_date 2012/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the rigidity results for self-shrinkers in Euclidean space by restriction of the image under the Gauss map. The geometric properties of the target manifolds carry into effect. In the self-shrinking hypersurface situation Theorem 3.1 and Theorem 3.2 not only improve the previous results, but also are optimal. In higher codimensional case, using geometric properties of the Grassmanian manifolds (the target manifolds of the Gauss map) we give a rigidity theorem for self-shrinking graphs.

Citations

• Rigidity of Entire self-shrinking solutions to curvature flows
• Generic mean curvature flow I; generic singularities

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• Rigidity Results for Spacelike Self-Shrinkers via Different Maximum Principles
• Some results on space-like self-shrinkers
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