Poincaré index and the volume functional of unit vector fields on punctured spheres

Fabiano G. B. Brito, André O. Gomes, Icaro Gonçalves

For $n\ge 1$, we exhibit a lower bound for the volume of a unit vector field on ${\mathbb{S}}^{2n+1}\backslash \{\pm p\}$ depending on the absolute values of its Poincaré indices aro…