Equivariant harmonic maps depend real analytically on the representation

Abstract

We consider harmonic maps into symmetric spaces of non-compact type that are equivariant for representations that induce a free and proper action on the symmetric space. We show that under suitable non-degeneracy conditions such equivariant harmonic maps depend in a real analytic fashion on the representation they are associated to. The main tool in the proof is the construction of a family of deformation maps which are used to transform equivariant harmonic maps into maps mapping into a fixed target space so that a real analytic version of the results in [4] can be applied.