  We prove that the Gauss map of a surface of constant mean curvature embedded
in Minkowski space is harmonic. This fact will then be used to study 2+1
gravity for surfaces of genus higher than one. By considering the energy of the
Gauss map, a canonical transform between the ADM reduced variables and holonomy
variables can be constructed. This allows one to solve (in principle) for the
evolution in the ADM variables without having to explicitly solve the
constraints first.
