Harmonic maps with noncontact boundary values

Every rank one symmetric space $M$, of noncompact type, admits a compactification $\overline M$ by attaching a sphere $S^{n-1}$ at infinity. If $M$ does not have constant sectional curvature, then $\overline M-M$ admits a natural contact structure. This paper presents a number of harmonic maps $h$, from $M$ to $M$, which extend continuously to $\overline M$, and have noncontact boundary values. If the boundary values are assumed continuously differentiable, then the contact structure must be preserved.