Stochastic Characterization of Harmonic maps on Riemannian polyhedra

Abstract

We have completely rewritten the paper, and corrected the proofs. We construct an exponential map at any point in the (n-1)-skeleton minus the (n-2)-skeleton of an n-dimensional Riemannian polyhedron. We have added allover the extra-assumption that the exponential map is totally geodesic at points in the (n-1)-skeleton minus the (n-2)-skeleton. This condition is automatically realized for instance if the dimension is one, or if the metric is flat.