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

2020/11/10 by Fabiano Brito, Brito, Fabiano, Jackeline Conrado +6 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #math.DG

paper · pdf · doi:10.48550/arxiv.2011.05183

arxiv created 2020/11/10 · arxiv updated 2020/11/11

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. In addition, for minimizing vector fields having specific pair of indexes, we show that their image coincides with the image of minimally immersed Klein bottles.

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

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