Moduli space theory for constant mean curvature surfaces immersed in   space-forms
  A new method is presented for solving the Gauss-Codazzi equations for a compact Riemann surface to be immersed in a 3-manifold of constant curvature. In the negative curvature case, the moduli for such embeddings are cohomology classes of (0,2) forms. 
Alexandre C. Goncalves and Karen K. Uhlenbeck