Mean curvature flow through singularities

2025/10/01 by Haslhofer, Robert
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.01355

Abstract

We first give a general introduction to the mean curvature flow, and then discuss fundamental results established over the last 10 years that yield a precise theory for the flow through singularities in ℝ³. With the aim of developing a satisfying theory in higher dimensions, we then describe our recent classification of all noncollapsed singularities in ℝ⁴. Finally, we provide a detailed discussion of open problems and conjectures.

Citations

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Related

• Generic mean curvature flow I; generic singularities
• On the non-degenerate and degenerate generic singularities formed by mean curvature flow
• Singularity structure in mean curvature flow of mean convex sets
• Lectures on mean curvature flow of surfaces
• Existence of Mean Curvature Flow Singularities with Bounded Mean Curvature