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

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