John圆的可分解性质和拟圆的一个充要条件

Decomposable Property of John Disks and a Sufficient and Necessary Condition of Quasidisks

证明D-R2是John圆当且仅当D具有John可分解性质;D-R2是拟圆当且仅当对于任意的z1,z2∈D,存在常数c≥1,使得1cλD(z1,z2)≤λD*(z1,z2)≤cλD(z1,z2).

We proved that D belong to R^2 is a John disk if and only if D has the John decomposable property, and that D belong to R^2 is a quasidisk if and only if for anyz1,z2∈δD, there exists a constant c≥1, such that 1/cλD（z1,z2）≤λD＊（z1,z2）≤cλD（z1,z2）.