The Weierstrass–Enneper Representation using Hodographic Coordinates on a Minimal Surface

[摘要] In this paper we obtain the general solution to the minimal surface equation, namely its local Weierstrass–Enneper representation, using a system of hodographic coordinates. This is done by using the method of solving the Born–Infeld equations by Whitham. We directly compute conformal coordinates on the minimal surface which give the Weierstrass–Enneper representation. From this we derive the hodographic coordinate $ρ in D subset mathbb{C}$ and 𝜎 its complex conjugate which enables us to write the Weierstrass–Enneper representation in a new way.

[学科分类] 数学（综合）

[关键词] Minimal surface;hodographic coordinates;conformal coordinates;Weierstrass–Enneper representation