Curve-shortening flow

Summary

The curve-shortening flow moves each point of a plane curve along its normal vector. The speed is the curvature of the curve at that point. It is the one-dimensional case of mean curvature flow and the steepest descent flow for the length of the curve. A heat-equation-like smoothing effect makes curves rounder over time, and embedded closed curves shrink to round points by the Gage–Hamilton–Grayson theorem.