In paper [2] we can find growth theorems for quasihomographies of the real line with three poiots (x1, x2, ∞) fixed. Those estimatioos were given for x > x1. ln this paper we give the estimations for x < x1.
In the paper some extremal normalization for the functionals denned on a Teichmiiller space of all quasiconformal automorphisms os the unit disc are investigated.
For alpha is an element of R, we find the linear-invariant order for functions g(z) = integralz/0 f'(t)(f(t)/t)alpha dt where f(z) = z+.... are holomorphic and univalent in the unit disk.
Authors gives new models of universal Teichmiiller space using so--called sewing theorem and some geometrical constructions connecting Jordan curves with quasiconformal automorphisms of unit circle.