Hamilton's geometric heat equation that proved the Poincaré conjecture
Initial Geometry
Flow Control
Curvature
Max K: 0 Min K: 0 Avg K: 0 Variance: 0
About
Ricci flow: ∂g_ij/∂t = −2R_ij
The metric evolves proportional to minus the Ricci curvature — like a geometric heat equation that diffuses curvature, smoothing bumpy geometries.
Hamilton (1982) introduced it. Perelman (2002-03) used it with surgery to prove the Poincaré conjecture: every simply-connected closed 3-manifold is homeomorphic to S³.
This visualizes the flow on a 2D surface embedded in 3D. High curvature regions (bright) are smoothed away.