It is proved that Kq(h)=K0(h) for every h in some class of quasisymmetric mappings of the unit circle with substantial points, where Kq(h):=sup{M(h(Q))/M(Q); Qis a quadrilateral with the domain unit disk} and K0(h) is...
Two necessary and sufficient conditions for the validity of the conjecture K 0(h)=K 1(h) are given, which are independent of the complex dilatations of extremal quasiconformal mappings, where K 0(h) is the maximal con...
LET D be the unit disk in the complex plane C and f be a sense preserving quasisymmetrichomeomorphism of D onto itself. Denote by Q a quadrilateral D (z1, z2, z3, z4 ) wit...
Let S0 be a compact Riemann surface with genus g,g>1. For any compact Riemannsurface S and any orientation preserved homeomorphism f:S0→S, we denote the pair (S,f) a marked Riemann surface....