Singular set and curvature blow-up rate of the level set flow

2022/11/21 by Siao-Hao Guo, Guo, Siao-Hao
Mathematics · #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2211.11464

Abstract

Under certain conditions such as the 2-convexity, a singularity of the level set flow is of type I (in the sense that the rate of curvature blow-up is constrained before and after the singular time) if and only if the flow shrinks to either a round point or a C¹ curve near that singular point. Analytically speaking, the arrival time is C² near a critical point if and only if it satisfies a Lojasiewicz inequality near the point.

Related

• Generic regularity of Level Set Flows with spherical singularity
• Mean Curvature Flow from Conical Singularities
• Type I singularities in the curve shortening flow associated to a density
• Blow-up Continuity for Type-I, Mean-Convex Mean Curvature Flow
• Stability and singular set of the two-convex level set flow