A Liouville Theorem for Mean Curvature Flow

2017/11/07 by Kevin Sonnanburg, Sonnanburg, Kevin
Mathematics · #53C44 #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.1711.02261

openalex publication_date 2017/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Ancient solutions arise in the study of parabolic blow-ups. If we can categorize ancient solutions, we can better understand blow-up limits. Based on an argument of Giga and Kohn, we give a Liouville-type theorem restricting ancient, type-I, non-collapsing two- dimensional mean curvature flows to either spheres or cylinders.

Related

• A Liouville type theorem for ancient Lagrangian mean curvature flows
• Blow Up of Compact Mean Curvature Flow Solutions with Bounded Mean Curvature
• Ancient solutions of the mean curvature flow
• On the blow-up analysis at collapsing poles for solutions of singular Liouville type equations
• Planarity and convexity for pinched ancient solutions of mean curvature flow