Removability of singularities of harmonic maps into pseudo-Riemannian manifolds

Frédéric Hélein (1)

1 CMLA - Centre de Mathématiques et de Leurs Applications

We consider harmonic maps into pseudo-Riemannian manifolds. We show the removability of isolatedsingularities for continuous maps, i.e. that any continuous map from an open subset of R^m into apseudo-Riemannian manifold which is two times continuously differentiable and harmonic everywhere outside anisolated point is actually smooth harmonic everywhere.

Mots clés: Partial differential equations of elliptic type; Non-Euclidean differential geometry

Domaines: Equations aux dérivées partielles [math.AP]; Géométrie différentielle [math.DG]

Frédéric Hélein. Removability of singularities of harmonic maps into pseudo-Riemannian manifolds. 2003. ⟨hal-00000360⟩