Area Minimizing Unit Vector Fields on Antipodally Punctured Unit 2-Sphere

Abstract

We provide a lower value for the volume of a unit vector field tangent to an antipodally Euclidean sphere ${\mathbb{S}}^2$ depending on the length of an ellipse determined by the indexes of its singularities.

This paper concerns a new version of Theorem 1 in arXiv:2011.05183. An updated version of Theorem 2 in the same paper will appear very soon on another submission