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arXiv · 2304.02487

Singularities of low entropy high codimension curve shortening flow

Florian Litzinger
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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.

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Florian Litzinger. 2023-04-05. Singularities of low entropy high codimension curve shortening flow. https://arxiv.org/abs/2304.02487

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