Let be a closed surface of genus at least , and let and be two laminations that fill . Let and be the right earthquakes on and , respectively. We show that the composition has a fixed point in the Teichmüller space of . Another way to state this result is that it is possible to prescribe any two measured laminations that fill a surface as the upper and lower measured bending laminations of the convex core of a globally hyperbolic anti-de Sitter (AdS) manifold. The proof uses some estimates from the geometry of those AdS manifolds.
"Fixed points of compositions of earthquakes." Duke Math. J. 161 (6) 1011 - 1054, 15 April 2012. https://doi.org/10.1215/00127094-1548434