Asymptotic Behavior and Stability of Mean Curvature Flow with a Conical End

2019/09/14 by Siao-Hao Guo, Guo, Siao-Hao
Mathematics · Physics and Astronomy · #53C44 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1909.06601

openalex publication_date 2019/09/14 · openalex created_date 2019/09/19 · openalex updated_date 2026/07/28

Abstract

If the initial hypersurface of an immortal mean curvature flow is asymptotic to a regular cone whose entropy is small, the flow will become asymptotically self-expanding. Moreover, the expander that gives rise to the limiting flow is asymptotically stable as an equilibrium solution of the normalized mean curvature flow.

Citations

• Smooth compactness for spaces of asymptotically conical self-expanders of mean curvature flow

Related

• Stability of mean convex cones under mean curvature flow
• A mountain-pass theorem for asymptotically conical self-expanders
• Self-expanders of the mean curvature flow
• On the Existence and Uniqueness of Ancient Rescaled Mean Curvature Flows
• Generic Dynamics of Mean Curvature Flows with Asymptotically Conical Singularities