Harmonic maps from \(\mathbb R^ n\) to \(\mathbb H^ m\) with symmetry. (Q700644)

Harmonic maps from \(\mathbb{R}^n\) to \(\mathbb{H}^m\) are constructed by prescribing boundary data at infinity, with some symmetry of the boundary data. The basic case to start with is \(m=n=2\), which plays the central role in the paper. But the maps for higher dimensions are not trivial modifications of the two-dimensional case. For the case \(m=n=2\), connections between the Hopf differential and the geometry of the image of the harmonic maps are studied.