Finsler Laplacians and minimal-energy maps

For any Finsler manifold, there is a geometrically natural Laplacian operator, called the mean-value Laplacian, which generalizes the Riemannian Laplacian. We show that, like the Riemannian Laplacian (for functions), we can see the vanishing of the mean-value Laplacian at some function f as the minimizing of an energy functional e(f) by f. This energy functional e depends on a Riemannian metric canonically associated to the Finsler metric and on a canonically associated Volume form. We relate this construction to a more general construction of Jest, and define a notion of harmonic mappings between Finsler manifolds.