In the paper we study the range of the system of functionals (|f(z₁)|, |f(z₂)|) over the class of K-quasiconformal homeomorphisms of the Riemann sphere with standard three point normalization f(0) = 0 ...

Given a circle pattern on the Riemann sphere ℂ̂, in this paper we prove that its quasiconformal deformation space can be naturally identified with the product of the Teichmüller spaces of its ...