Ricci Flow — Surface Evolution

Hamilton 1982: ∂g/∂t = −2 Ric(g) · smooth surfaces toward constant curvature

t = 0.000
Max |K| = 0.000
Variance = 0.000
Ricci flow deforms a Riemannian metric proportional to its Ricci curvature tensor, smoothing out geometrical bumps. Hamilton proved round spheres are the only compact 3-manifolds of positive Ricci curvature — the key step toward Perelman's proof of the Poincaré conjecture. Colors: red = positive curvature, blue = negative curvature.