Decomposition of extremal length and a proof of Shen’s conjecture on QED constant and boundary dilatation

In this paper we study the relations among various constants of quasiextremal distance (QED) domains in the plane. In particular, we give an affirmative answer to Shen’s conjecture about the relation between the QED constant (Ω)and the boundary dilatation(Ω).This leads to the conclusion that, for a large class of domains, the equality M(Ω)1Ω conjectured by Garnett and Yang does not hold, where Ω is the quasiconformal reflection constant.