Truncations of extremal quasiconformal mappings and their applications

In this paper we give a necessary and sufficient condition to decide whether the Teichmüller equivalency class [α] of a truncation α induced by a uniquely extremal Beltrami differential is a Strebel point in T. We also obtain a necessary and sufficient condition of the unique extremality of α. Using the properties of truncations we provide a method to construct Hamilton sequences. We also get a sufficient condition for the extremality of f(z,t) to be equivalent to that of F(w,t). The corresponding results in the infinitesimal case are obtained, too.