A cyclic extension of the earthquake flow II

The landslide flow is a smoother analog of the earthquake ow on Teichmuller space which shares some of its key properties. We show here that further properties of earthquakes apply to landslides. The landslide ow is the Hamiltonian flow of a convex function. The smooth grafting map sgr taking values in Teichmuller space, which is to landslides as grafting is to earthquakes, is proper and surjective with respect to either of its variables. The smooth grafting map SGr taking values in the space of complex projective structures is symplectic (up to a multiplicative constant). The composition of two landslides has a fixed point on Teichmuller space. As a consequence we obtain new results on constant Gauss curvature surfaces in 3-dimensional hyperbolic or AdS manifolds. We also show that the landslide flow has a satisfactory extension to the boundary of Teichmuller space.