2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59301Non-polynomial growth harmonic maps from the complex plane to the hyperbolic space are studied. Some non-surjectivity results are obtained. Moreover, images of such harmonic maps are investigated with reference to their Hopf differentials.49 pages, 7 groups of figures, revised edition, no offset problem. To appear in Communication Analysis and GeometryDifferential Geometrytext