In the paper some extremal normalization for the functionals denned on a Teichmiiller space of all quasiconformal automorphisms os the unit disc are investigated.
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.
In the paper some harmonic quadrilaterals to the given quadrilaterals are investigated. Every vertex of such harmonic quadrilaterals is the harmonic center of three vertex given quadrilateral.
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