Comunicació presentada a: 6th Pacific-Rim Symposium on Image and Video Technology Workshop, celebrat del 28-29 d'octubre de 2013 a Guanajuato, Mèxic. We present a method to perform histogram matching be- tween two color images based on the concept of harmonic mapping be- tween Riemannian manifolds. The key idea is to associate the histogram of a color image to a Riemannian manifold. In this context, the energy of the matching between the two images is measured by the Dirichlet energy of the mapping between the Riemannian manifolds. Then, we assimilate optimal matchings to critical points of the Dirichlet energy. Such points are called harmonic maps. As there is no explicit expression for harmonic maps in general, we use a gradient descent ow with boundary condition to reach them, that we call harmonic ow. We present an application to color transfer, however many others applications can be envisaged using this general framework. This work was supported by European Research Council, Starting Grant ref. 306337. The second author acknowledges partial support by Spanish grants AACC, ref. TIN2011-15954-E, and Plan Nacional, ref. TIN2012-38112.