A mean value inequality for the generalized self-expander type submanifolds and its application

2015/03/15 by Liang Cheng, Cheng, Liang
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #math.DG

paper · pdf · doi:10.48550/arxiv.1503.04437

arxiv created 2015/03/15 · openalex publication_date 2015/03/15 · arxiv updated 2015/03/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper we get a version of mean value inequality for generalized self-expander type submanifolds in Euclidean space. As the application, we prove that if mean curvature flow M(t) on the self-expander in Euclidean space subconverges to an n-rectifiable varifold T in weak sense for t goes to the singular time, then T must be the cone.

Citations

• Asymptotic behavior of Type III mean curvature flow on noncompact hypersurfaces
• Bernstein theorem for translating solitons of hypersurfaces

Related

• Mean curvature flow in submanifolds
• Self-expanders of the mean curvature flow
• Convexity of mean convex asymptotically conical self-expanders to the mean curvature flow
• Volume properties and rigidity on self-expanders of mean curvature flow
• Asymptotic behavior of Type III mean curvature flow on noncompact hypersurfaces