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,the...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.展开更多
基金Sponsored by the Foundation of Pre-973 Program of China under grant2006CB708304the National NSFC under grant 10771195the NSF of Zhejiang Province under grant Y607128
文摘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.
