Local and global well-posedness of wave maps on ¹⁺¹ for rough data

We prove local and global existence from large, rough initial data for a wave map between 1+1 dimensional Minkowski space and an analytic manifold. Included here is global existence for large data in the scale-invariant norm L1,1, and in the Sobolev spaces Hˢ for $s > 3/4$. This builds on previous work in 1+1 dimensions of Pohlmeyer, Gu, Ginibre-Velo and Shatah.