2003/09/30 by Rukmini Dey
Mathematics · #math.DG #math.AP
published as Proc. Indian Acad. Sci. (Math. Sci.), Vol. 113, No. 2, May 2003, pp. 189-193 · 5-pages, semi-expository article, published in Proceedings of the Indian Academy of Sciences, 2003 (an electronic journal)
arxiv created 2004/04/03 · arxiv updated 2009/12/01
In this paper we obtain the general solution to the minimal surface equation, namely its local Weierstrass-Enneper representation, by 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 ⊂ \CC and σ its complex conjugate which enables us to write the Weierstrass-Enneper representation in a new way.