Geometry and Topology Seminar

The Teichmüller space of a Riemann surface is the space of quasiconformal deformations of its complex structure. For a compact surface, Thurston introduced a celebrated compactification of its Teichmüller space by adding a boundary consisting of measured geodesic laminations on the surface. We introduce a similar boundary for noncompact surfaces such as the open disk, by considering the Liouville measures of quasiconformal deformations of the Riemann surface and their degenerations to measured geodesic laminations. This analysis requires the introduction and control of certain uniformity conditions, which are automatic in the compact case. This is joint work with Dragomir Saric.