Curve-shortening flow

In mathematics, the curve-shortening flow is a type of geometric flow. It is the special case of the mean curvature flow where the evolving Riemannian manifold is one-dimensional. Its name derives from the fact that it is the steepest-descent flow for the length functional. If the initial manifold is compact, it will become extinct in finite time at a round singularity by general results of Huisken, but non-compact initial data may yield solitons.

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