Global regularity of wave maps from $R^{3+1}$ to surfaces

We consider Wave Maps with smooth compactly supported initial data of small (H) over dot (3/2)-norm from R3+1 to certain 2-dimensional Riemannian manifolds and show that they stay smooth globally in time. Our methods are based on the introduction of a global Coulomb Gauge as in [17], followed by a dynamic separation as in [8]. We then rely on an adaptation of T. Tao's methods used in his recent breakthrough result [24].