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

2021/02/22 by Fabiano Brito, Fabiano G. B. Brito, Jackeline Conrado +7
Engineering · Mathematics · #Aerospace Engineering and Control Systems #Differential Geometry (math.DG) #Ellipse #Euclidean geometry #Euclidean space #FOS: Mathematics #Field (mathematics) #Geometry #Gravitational singularity #Material Science and Thermodynamics #Mathematical analysis #Mathematics #Point processes and geometric inequalities #Pure mathematics #Tangent #Unit (ring theory) #Unit sphere #Unit vector #Vector field #math.DG

paper · pdf · doi:10.48550/arxiv.2102.11128

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

arxiv created 2021/02/22 · openalex publication_date 2021/02/22 · arxiv updated 2021/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We provide a lower value for the volume of a unit vector field tangent to an antipodally Euclidean sphere \mathbbS² depending on the length of an ellipse determined by the indexes of its singularities.

Citations

• Area minimizing unit vector fields on antipodally punctured unit 2-sphere and minimally immersed Klein Bottles

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