Compactness for immersions of prescribed Gaussian curvature II - geometric aspects

We develop a compactness result near the boundary for families of locally convex immersions. We also develop a mod 2 degree theory for immersion of constant (and prescribed) Gaussian curvature with prescribed boundary. These are then used to solve the Plateau problem for immersions of constant (and prescribed) Gaussian curvature in general Hadamard manifolds.