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arXiv · 1808.03936

Sharp Entropy Bounds for Plane Curves and Dynamics of the Curve Shortening Flow

Julius Baldauf·Ao Sun
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Abstract

We prove that a closed immersed plane curve with total curvature $2πm$ has entropy at least $m$ times the entropy of the embedded circle, as long as it generates a type I singularity under the curve shortening flow (CSF). We construct closed immersed plane curves of total curvature $2πm$ whose entropy is less than $m$ times the entropy of the embedded circle. As an application, we extend Colding-Minicozzi's notion of a generic mean curvature flow to closed immersed plane curves by constructing a piecewise CSF whose only singularities are embedded circles and type II singularities.

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Julius Baldauf, Ao Sun. 2020-12-25. Sharp Entropy Bounds for Plane Curves and Dynamics of the Curve Shortening Flow. https://arxiv.org/abs/1808.03936

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