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…