10 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…
Poincaré index and the volume functional of unit vector fields on punctured spheres
Fabiano G. B. Brito, André O. Gomes, Icaro Gonçalves
For , we exhibit a lower bound for the volume of a unit vector field on depending on the absolute values of its Poincaré indices aro…
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…
Degree of the Gauss map and curvature integrals for closed hypersurfaces
Fabiano G. B. Brito, Icaro Gonçalves
Given a unit vector field on a closed Euclidean hypersurface, we define a map from the hypersurface to a sphere in the Euclidean space. This application allows us to exhibit a list…