Minimal surfaces have zero mean curvature H = (κ₁+κ₂)/2 = 0.
They are critical points of the area functional — locally area-minimizing.
Weierstrass-Enneper:
x+iy = ∫(1-w²,i(1+w²),2w)f(w)dw
Surface: Enneper
Gaussian curvature K = κ₁·κ₂ ≤ 0
(saddle points everywhere)
They are critical points of the area functional — locally area-minimizing.
Weierstrass-Enneper:
x+iy = ∫(1-w²,i(1+w²),2w)f(w)dw
Surface: Enneper
Gaussian curvature K = κ₁·κ₂ ≤ 0
(saddle points everywhere)