5 papers
Area Minimizing Unit Vector Fields on Antipodally Punctured Unit 2-Sphere
Fabiano G. B. Brito, Jackeline Conrado, Icaro Gonçalves +1
We provide a lower value for the volume of a unit vector field tangent to an antipodally Euclidean sphere depending on the length of an ellipse determined by the ind…
Area minimizing unit vector fields on antipodally punctured unit 2-sphere and minimally immersed Klein Bottles
Fabiano Brito, Jackeline Conrado, Adriana Nicoli +1
We provide a lower value for the volume of a unit vector field tangent to an antipodally Euclidean sphere depending on the length of an ellipse determined by the ind…
Loxodromic unit vector field on punctured spheres
Jackeline Conrado, Adriana V. Nicoli, Giovanni N. Nunes
In these short notes we characterize the loxodromic unit vector fields on antipodally punctured Euclidean spheres as the only ones achieving a lower bound for the volume functional…
A topological lower bound for the energy of a unit vector field on a closed Euclidean hypersurface
Fabiano G. B. Brito, Icaro Gonçalves, Adriana V. Nicoli
For a unit vector field on a closed immersed Euclidean hypersurface , , we exhibit a nontrivial lower bound for its energy which depends on the degree of the Gau…
A topological lower bound for the energy of a unit vector field on a closed hypersurface of the euclidean space. The 3-dimensional case
Fabiano G. B. Brito, Andre O. Gomes, Adriana V. Nicoli
In this short note we prove that the degree of the Gauss map ν of a closed 3-dimensional hypersurface of the Euclidean space is a lower bound for the total bending functional B, in…