Area-minimizing unit vector fields on some spherical annuli

TL;DR

This paper derives a precise lower bound for the area of unit vector fields on spherical annuli in the Euclidean sphere, contributing to the understanding of geometric properties of vector fields on curved surfaces.

Contribution

It introduces a sharp lower bound for the area of unit vector fields specifically on spherical annuli, advancing geometric analysis in spherical domains.

Findings

Established a sharp lower bound for the area of unit vector fields.

Applied the bound to spherical annuli in the Euclidean sphere.

Enhanced understanding of geometric constraints on vector fields.

Abstract

We establish in this paper a sharp lower bound for the area of a unit vector field $V$ defined on some spherical annuli in the Euclidean sphere $\mathbb{S}^2$.