Global regularity of wave maps V. Large data local wellposedness and perturbation theory in the energy class

Using the harmonic map heat flow and the function spaces of Tataru and the author, we establish a large data local well-posedness result in the energy class for wave maps from two-dimensional Minkowski space $\R^{1+2}$ to hyperbolic spaces $\H^m$. This is one of the five claims required in an earlier paper in this series to prove global regularity for such wave maps.