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.
References
- Chou, Kai-Seng; Zhu, Xi-Ping (2001), The Curve Shortening Problem, Boca Raton, FL: Chapman & Hall/CRC, doi:10.1201/9781420035704, ISBN 1-58488-213-1, MR 1888641.