Minimal Surfaces from Monopoles

TL;DR

This paper explores the geometric relationship between charge 2 monopoles and minimal surfaces, revealing how monopole structure influences surface curvature and Gauss map behavior.

Contribution

It provides a detailed description of minimal surfaces generated by charge 2 monopoles using the moduli parameter k, linking monopole geometry to surface curvature.

Findings

Gaussian curvature distribution reflects monopole structure

Gauss maps illustrate monopole influence on surface geometry

Monopole moduli parameter k governs surface shape

Abstract

The geometry of minimal surfaces generated by charge 2 Bogomolny monopoles on 3-dimensional Euclidean space is described in terms of the moduli parameter k. We find that the distribution of Gaussian curvature on the surface reflects the monopole structure. This is elucidated by the behaviour of the Gauss maps of the minimal surfaces.