Explore how curves and surfaces evolve through 21 interactive demonstrations featuring curve shortening flow, mean curvature flow, Ricci flow, and the story of the Poincare conjecture.
See also: Differential Geometry for the curvatures these flows evolve, Differential Equations for the parabolic PDEs governing geometric evolution, and Topology for the topological changes Ricci flow can produce.
Temperature diffusion on curves and surfaces — the simplest geometric flow
Watch curves shrink to circles and vanish — the Gage-Hamilton-Grayson theorem
Surfaces evolving by mean curvature — soap films and singularity formation
Hamilton's flow that smooths the metric — the engine behind Perelman's proof
When flows break down — neckpinches, ancient solutions, and surgical repair
From Poincaré's question to Perelman's proof — topology through geometry
Compare flows side by side — Willmore, inverse MCF, and exotic evolutions