Area minimizing unit vector fields on antipodally punctured unit 2-sphere

Brito, Fabiano G. B.; Conrado, Jackeline; Gonçalves, Icaro; Nicoli, Adriana V.

doi:10.5802/crmath.258

Géométrie et Topologie

Area minimizing unit vector fields on antipodally punctured unit 2-sphere

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

Comptes Rendus. Mathématique, Tome 359 (2021) no. 10, pp. 1225-1232.

Résumé

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 ${\vec{v}}_{k}$ 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 $S$ .

Reçu le : 2021-02-18
Révisé le : 2021-05-20
Accepté le : 2021-08-11
Publié le : 2022-01-04

DOI : 10.5802/crmath.258

Affiliations des auteurs :

Brito, Fabiano G. B. ¹ ; Conrado, Jackeline ² ; Gonçalves, Icaro ¹ ; Nicoli, Adriana V. ²

@article{CRMATH_2021__359_10_1225_0,
     author = {Brito, Fabiano G. B. and Conrado, Jackeline and Gon\c{c}alves, Icaro and Nicoli, Adriana V.},
     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},
     url = {http://www.numdam.org/articles/10.5802/crmath.258/}
}

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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, Tome 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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