Nondegeneracy of harmonic maps from \mathbb R² to \mathbb S²

2018/06/11 by Guoyuan Chen, Yong Liu, Chen, Guoyuan +3
Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1806.04131

openalex publication_date 2018/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that all harmonic maps from \mathbb R² to \mathbb S² with finite energy are nondegenerate. That is, for any harmonic map u from \mathbb R² to \mathbb S² 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.

Citations

• Harmonic Mappings of Riemannian Manifolds

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