REMARKS ON JOHN DISKS

Let D■R2 be a Jordan domain,D*=R2\D,the exterior of D.In this article,the authors obtained the following results:(1)If D is a John disk,then D is an outer linearly locally connected domain;(2)If D* is a John disk,then D is an inner linearly locally connected domain;(3)A homeomorphism f:R 2 →R 2 is a quasiconformal mapping if and only if f(D)is a John disk for any John disk D■R 2 ;and(4)If D is a bounded quasidisk,then D is a John disk,and there exists an unbounded quasidisk which is not a John disk.     

平面K—拟共形映照Mori常数的一个改进值和两个偏差估计

本文改进了著名的关于平面K—拟共形映照中的H?lder连续性的Mori定理,得到了如下结果:设f为R~2中的单位园B~2到B~2的K—拟共形映照且满足f(o)=0,若令本文还利用了平面K—拟共形映照的参数表示法得到了如下两个新的偏差性质:设f为R~2中的单位园B~2到B~2的K—拟共形自映照,且满足f(o)=0,则有