Truncations of extremal quasiconformal mappings and their applications

In this paper we give a necessary and sufficient condition to decide whether the Teichmuller equivalency class [alpha] of a truncation alpha 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 alpha. 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. (c) 2006 Elsevier Inc. All rights reserved.