An existence result of energy minimizer maps between riemannian   polyhedra
  In this paper, we prove the existence of energy minimizers in each free homotopy class of maps between polyhedra with target space without focal points. Our proof involves a careful study of some geometric properties of riemannian polhyedra without focal points. Among other things, we show that on the relevant polyhedra, there exists a convex supporting function. 
Taoufik Bouziane