Equivariant harmonic maps depend real analytically on the representation

TL;DR

This paper proves that equivariant harmonic maps into symmetric spaces depend real analytically on the associated representation under certain conditions, using deformation maps to facilitate the analysis.

Contribution

It introduces a method to show real analytic dependence of harmonic maps on representations, extending previous results to a broader class of symmetric spaces.

Findings

Dependence of harmonic maps on representations is real analytic.

Construction of deformation maps enables the analysis.

Results apply to symmetric spaces of non-compact type.

Abstract

We prove that when assuming suitable non-degeneracy conditions equivariant harmonic maps into symmetric spaces of non-compact type 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 \cite{EellsLemaire} can be applied.