Nondegeneracy of harmonic maps from ${\mathbb{R}}^2$ to ${\mathbb{S}}^2$

Guoyuan Chen, Yong Liu, Juncheng Wei

We prove that all harmonic maps from ${\mathbb{R}}^2$ to ${\mathbb{S}}^2$ with finite energy are nondegenerate. That is, for any harmonic map $u$ from ${\mathbb{R}}^2$ to ${\mathbb{S}}^2$ of d…