• The Weierstrass—Enneper representation using hodographic coordinates on a minimal surface

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/113/02/0189-0193

    • Keywords

       

      Minimal surface; hodographic coordinates; conformal coordinates; Weierstrass-Enneper representation

    • 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.

    • Author Affiliations

       

      Rukmini Dey1

      1. School of Mathematics, Harish-Chandra Research Institute, Allahabad - 211 019, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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