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

      Rukmini Dey

      Volume 113 Issue 2 May 2003 pp 189-193

    • Fulltext

       

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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

       
      Published
      May 2003
      Manuscript received
      19 June 2002
      Manuscript revised
      10 October 2002

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