Singularities of low entropy high codimension curve shortening flow

2023/04/05 by Litzinger, Florian
#53E10 (Primary) 35K59 (Secondary) #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.02487

Abstract

We consider curve shortening flow of arbitrary codimension in an Euclidean background. We show that, close to a singularity, the flow is asymptotically planar, paralleling Altschuler's work in the case of space curves, and analyse the blow-up limits of the flow. Using these results, we then prove that the curve shortening flow of initial curves with an entropy bound converges to a round point in finite time.

Related

• Sharp Entropy Bounds for Plane Curves and Dynamics of the Curve Shortening Flow
• Uniqueness of tangent flows at infinity for finite-entropy shortening curves
• On bounds of entropy and total curvature for ancient curve shortening flows
• The blow up analysis of the general curve shortening flow
• The Curve Shortening Flow for Curves of Finite Total (Absolute) Curvature