Ricci Flow — Surface Geometry Smoothing
Hamilton's ∂g/∂t = −2 Ric(g): curvature-driven metric evolution on 2-manifolds
Surface & Flow
Surface type
Bumpy sphere
Dumbbell
Torus (flat → round)
Saddle
Flow time t =
0.00
Amplitude A =
1.0
Grid resolution =
30
Animate Flow
Reset t=0
Curvature
Mean K̄
—
Max |K|
—
Gauss-Bonnet ∫K dA
—
∂g_{ij}/∂t = −2 R_{ij}
Normalized: ∂g/∂t = −2(Ric − r̄g)
For 2D: R = scalar curvature
Converges to constant curvature
Proof of Poincaré conjecture (Perelman)