Abstract
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∈ D ⊂ ℂ and σ its complex conjugate which enables us to write the Weierstrass-Enneper representation in a new way.
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Dey, R. The Weierstrass—Enneper representation using hodographic coordinates on a minimal surface. Proc. Indian Acad. Sci. (Math. Sci.) 113, 189–193 (2003). https://doi.org/10.1007/BF02829769
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DOI: https://doi.org/10.1007/BF02829769