A correspondence between genus one minimal Lawson surfaces of $\mathbb{S}^3(2)$ and area-minimizing unit vector fields on the antipodally punctured unit 2-sphere

TL;DR

This paper explores a link between certain minimal surfaces in a 3-sphere and area-minimizing vector fields on a punctured 2-sphere, revealing stability properties of Lawson cylinders.

Contribution

It establishes a novel correspondence between genus one minimal Lawson surfaces in -geometry and minimal vector fields on a punctured sphere, connecting geometric analysis and variational problems.

Findings

Established a correspondence between minimal Lawson surfaces and vector fields.

Proved a stability relation for Lawson cylinders.

Linked minimal surface theory with vector field minimization.

Abstract

A correspondence is established between a class of minimal immersed surfaces of $\mathbb{S}^3(2)$ and area-minimizing unit vector fields defined on the antipodally punctured unit sphere $\mathbb{S}^2\backslash\{N,S\}$. As a consequence, we establish a stability relation for Lawson cylinders in $\mathbb{S}^3(2)$.