Stochastic Characterization of Harmonic maps on Riemannian polyhedra
Probability
2007-06-13 v3 Differential Geometry
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.
Cite
@article{arxiv.math/0503557,
title = {Stochastic Characterization of Harmonic maps on Riemannian polyhedra},
author = {M. A. Aprodu and T. Bouziane},
journal= {arXiv preprint arXiv:math/0503557},
year = {2007}
}