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
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
In this article,we first establish an asymptotically sharp Koebe type covering theorem for harmonic K-quasiconformal mappings.Then we use it to obtain an asymptotically Koebe type distortion theorem,a coefficients est...In this article,we first establish an asymptotically sharp Koebe type covering theorem for harmonic K-quasiconformal mappings.Then we use it to obtain an asymptotically Koebe type distortion theorem,a coefficients estimate,a Lipschitz characteristic and a linear measure distortion theorem of harmonic K-quasiconformal mappings.At last,we give some characterizations of the radial John disks with the help of pre-Schwarzian of harmonic mappings.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.
基金Sponsored by the Foundation of Pre-973 Program of China under grant2006CB708304+2 种基金 the National NSFC under grant 10771195 the 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.
基金National Natural Science Foundation of China(Grant No.12071116)the Key Projects of Hunan Provincial Department of Education(Grant No.21A0429)+3 种基金the Discipline Special Research Projects of Hengyang Normal University(Grant No.XKZX21002)the Science and Technology Plan Project of Hunan Province(Grant No.2016TP1020)the Application-Oriented Characterized Disciplines,Double First-Class University Project of Hunan Province(Xiangjiaotong[2018]469)Mathematical Research Impact Centric Support(MATRICS)of the Department of Science and Technology(DST),India(MTR/2017/000367).
文摘In this article,we first establish an asymptotically sharp Koebe type covering theorem for harmonic K-quasiconformal mappings.Then we use it to obtain an asymptotically Koebe type distortion theorem,a coefficients estimate,a Lipschitz characteristic and a linear measure distortion theorem of harmonic K-quasiconformal mappings.At last,we give some characterizations of the radial John disks with the help of pre-Schwarzian of harmonic mappings.
