1549055259-Ubiquitous_Quasidisk__The__Gehring_

CHAPTER 10

Third series of implications

We establish here three more characterizations for quasidisks making use of the
following result established in Chapter 8 :

D is a quasidisk if and only if it has the hyperbolic segment property.

We prove, in particular, the following two chains of statements for a simply con-
nected domain D.

1° A quasidisk is a EMO-extension domain.

2° The inequality hn ::;: cjn holds in a EMO-extension domain.

3° The inequality hn ::;: cjn implies the segment property.

4° The inequaltiy hn::;: can holds in a quasidisk.

5° The inequality hv ::;: c av implies the hyperbolic segment property.

D is a quasidisk

7

D has EMO-

extension property

10.2 t

hv :S: cfo

~

8.2-8.6

hv :S: cfo

7

D has the hyperbolic

segment property

FIGURE 10.l

137