An Enneper-Weierstrass Minimal Surface
An Enneper-Weierstrass Minimal Surface
A minimal surface has zero mean curvature. An Enneper-Weierstrass parametrization for such a surface is based on two suitably defined holomorphic functions and . The functions chosen here are and . Embedding in is given by the indefinite integrals =∫(z)z, where =f(z)1-, =f(z)1+ and =2f(z)g(z). The surface shown is the parametric plot of the real and imaginary parts of the as ranges over an annulus.
f(z)
g(z)
f(z)=+
1/r
z
z
z
g(z)=z
3
x
k
ϕ
k
ϕ
1
2
g(z)
ϕ
2
2
g(z)
ϕ
3
x
k
z