  This paper is a study of harmonic maps from Riemannian polyhedra to (locally)
non-positively curved geodesic spaces in the sense of Alexandrov. We prove
Liouville-type theorems for subharmonic functions and harmonic maps under two
different assumptions on the source space. First we prove the analogue of the
Schoen-Yau Theorem on a complete (smooth) pseudomanifolds with non-negative
Ricci curvature. Then we study 2-parabolic admissible Riemannian polyhedra and
prove some vanishing results on them.
