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
Extrinsic geometric flows are flows on embedded submanifolds, or more generally immersed submanifolds. In general they change both the Riemannian metric and the immersion.
- Mean curvature flow, as in soap films; critical points are minimal surfaces
- Willmore flow, as in minimax eversions of spheres
Intrinsic
Intrinsic geometric flows are flows on the Riemannian metric, independent of any embedding or immersion.
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)