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

• # Fulltext

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

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

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 4
September 2019