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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

, where

and

. The surface shown is the parametric plot of the real and imaginary parts of the

ranges over an annulus.

Contributed by: Michael Schreiber

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Minimal Surface (Wolfram MathWorld)

Isothermal Parameterization (Wolfram MathWorld)

Enneper-Weierstrass Parameterization (Wolfram MathWorld)

"An Enneper-Weierstrass Minimal Surface" from the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/AnEnneperWeierstrassMinimalSurface/

Contributed by: Michael Schreiber

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An Enneper-Weierstrass Minimal Surface

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