Quasiextremal Distance Constants And Quasiconformal Boundary Dilatation

In this paper we study QED constants M-2,2 in the complex plane, especially, we study the relation between the QED constants M2,2 and the boundary dilatation H(Ω). When M2,2 is attained by degenerate continuas An and Bn, by analyzing the critical points and level sets of harmonic function, we suppose then the upper bound of M2,2 is controlled by the boundary dilatation H(Ω), so we get the following result:in complex plane C, suppose Ω is a Jordan domain, if M2,2(Ω) is obtained by a pair of disjoint degenerate continuas An, Bn(here An= An1∪An2, Bn= Bn1∪Bn2), that is and then we have M2,2(Ω)≤1+H(Ω).