Comptes Rendus
Géométrie et Topologie
Area minimizing unit vector fields on antipodally punctured unit 2-sphere
Fabiano G. B. Brito1 ; Jackeline Conrado2 ; Icaro Gonçalves1 ; Adriana V. Nicoli2
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
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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DOI : 10.5802/crmath.258
Fabiano G. B. Brito 1 ; Jackeline Conrado 2 ; Icaro Gonçalves 1 ; Adriana V. Nicoli 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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@article{CRMATH_2021__359_10_1225_0,
     author = {Fabiano G. B. Brito and Jackeline Conrado and Icaro Gon\c{c}alves and Adriana V. Nicoli},
     title = {Area minimizing unit vector fields on antipodally punctured unit 2-sphere},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1225--1232},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {10},
     year = {2021},
     doi = {10.5802/crmath.258},
     language = {en},
}
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Fabiano G. B. Brito; Jackeline Conrado; Icaro Gonçalves; Adriana V. Nicoli. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.258/

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