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

Guoyuan Chen; Yong Liu; Juncheng Wei

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arXiv · 1806.04131

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

Guoyuan Chen·Yong Liu·Juncheng Wei

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Abstract

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 degree $m$ (in $\mathbb Z$), all bounded kernel maps of the linearized operator $L_u$ at $u$ are generated by these harmonic maps near $u$ and hence the real dimension of bounded kernel space of $L_u$ is $4|m|+2$.

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Guoyuan Chen, Yong Liu, Juncheng Wei. 2018-06-11. Nondegeneracy of harmonic maps from $\mathbb R^2$ to $\mathbb S^2$. https://arxiv.org/abs/1806.04131

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