Geometry and Topology
Area minimizing unit vector fields on antipodally punctured unit 2-sphere
Comptes Rendus. Mathématique, Volume 359 (2021) no. 10, pp. 1225-1232.

We provide a lower value for the volume of a unit vector field tangent to an antipodally punctured Euclidean sphere 𝕊 2 depending on the length of an ellipse determined by the indexes of its singularities. We also exhibit minimizing vector fields v k within each index class and show that they are the only ones that are sharp for the volume. These fields have areas given essentially by the length of ellipses depending just on the indexes in N and S.

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Accepted:
Published online:
DOI: 10.5802/crmath.258
Brito, Fabiano G. B. 1; Conrado, Jackeline 2; Gonçalves, Icaro 1; Nicoli, Adriana V. 2

1 Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, Santo André, 09210-170, Brazil
2 Dpto. de Matemática, Instituto de Matemática e Estatística, Universidade de São Paulo, R. do Matão 1010, São Paulo-SP, 05508-900, Brazil
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     title = {Area minimizing unit vector fields on antipodally punctured unit 2-sphere},
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Brito, Fabiano G. B.; Conrado, Jackeline; Gonçalves, Icaro; Nicoli, Adriana V. Area minimizing unit vector fields on antipodally punctured unit 2-sphere. Comptes Rendus. Mathématique, Volume 359 (2021) no. 10, pp. 1225-1232. doi : 10.5802/crmath.258. http://www.numdam.org/articles/10.5802/crmath.258/

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