1549055259-Ubiquitous_Quasidisk__The__Gehring_

8.8. QUASIDISKS AND DECOMPOSABILITY

hyperbolic segment/ joining z 1 and z 2 in D' CD such that for each z E /,

length(!) :::; c lz1 - z2I,

min length(lj):::; cdist(z,8D).

J=l, 2

115

Here 11, 12 are the components of / \ { z} and c = c( K'). Thus D is a simply
connected uniform domain and hence a K-quasidisk where K depends only on
~. D