Ricci Flow on Surfaces

Hamilton's Ricci flow: ∂g/∂t = −2 Ric(g). On a 2D surface, the scalar curvature R evolves by ∂R/∂t = ΔR + R². The metric uniformizes toward constant curvature — the basis of Perelman's proof of the Geometrization Conjecture.

Scalar Curvature R(x,y,t)

Conformal Factor e^u (metric distortion)

Diffusion Speed 1.0

Initial Bump Height 2.0

Initial Shape

t = 0.000 | R_max = 0.000 | R_min = 0.000