Surface Type
Properties
Mean curvature H≡ 0
Gauss curvature K—
Topology χ—
Self-intersections—
Theory
Minimal surface: H = 0
H = (κ₁ + κ₂)/2 = 0
(principal curvatures cancel)
Weierstrass-Enneper:
x + iy = ∫f(1−g²) + if(1+g²) + 2fg dw
Physical: soap film minimizes area between wire boundaries — Laplace pressure ΔP = 2γH = 0