Homotopy problems for harmonic maps to spaces of nonpositive curvature

Two results by N.J. Korevaar and R. M. Schoen ( 1993) about solvability of the free homotopy problem and the Dirichlet homotopy problem for harmonic maps from a compact Riemannian manifold X to a compact geodesic space Y of nonpositive curvature are strengthened here, and extended, particularly by allowing X to be any compact admissible Riemannian polyhedron. In that setting, the two results were stated in the author's monograph from 2001 with J. Eells, but the short proofs given there were incomplete.