Geometric flow

In mathematics, specifically differential geometry, a geometric flow is the gradient flow associated to a functional on a manifold which has a geometric interpretation, usually associated with some extrinsic or intrinsic curvature.

These are of fundamental interest in the calculus of variations, and include several famous problems and theories. Particularly interesting are their critical points.

Examples

Extrinsic

• Mean curvature flow, as in soap films; critical points are minimal surfaces
• Willmore flow, as in minimax eversions of spheres

Intrinsic

• Ricci flow, as in the Hamilton–Perelman solution of the Poincaré conjecture
• Calabi flow

References

• Bakas, I. "The algebraic structure of geometric flows in two dimensions". arXiv eprint server. Retrieved July 28. {{cite web}}: Check date values in: |accessdate= (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help)