Earthquakes and Graftings of Hyperbolic Surface laminations

We study compact hyperbolic surface laminations. These are a generalisation of closed hyperbolic surfaces, which appear to be more suited to the study of Teichmüller theory than arbitrary non-compact surfaces. We show that the Teichmüller space of any non-trivial hyperbolic surface lamination is infinite dimensional. In order to prove this result, we study the theory of deformations of hyperbolic surfaces, and we derive a new formula for the derivative of the length of a simple closed geodesic with respect to the action of grafting. This formula complements those derived by McMullen [ 24], in terms of the Weil–Petersson metric, and by Wolpert [ 34], for the case of earthquakes.