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REMARKS ON JOHN DISKS

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【Author】 Chu Yuming Department of Mathematics,Huzhou Teachers College,Huzhou 313000,China Cheng Jinfa Department of Mathematics,Xiamen University,Xiamen 361005,China Wang Gendi Department of Mathematics,Huzhou Teachers College,Huzhou 313000,China

【机构】 Department of Mathematics, Huzhou Teachers College； Department of Mathematics, Xiamen University；

【摘要】 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.更多还原

【Abstract】 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.更多还原

【关键词】 John disks； Linearly locally connected domains； Quasiconformal mappings； Quasidisks；
【Key words】 John disks； Linearly locally connected domains； Quasiconformal mappings； Quasidisks；

【基金】 Sponsored by the Foundation of Pre-973 Program of China under grant2006CB708304;the National NSFC under grant 10771195;the NSF of Zhejiang Province under grant Y607128

【文献出处】 Acta Mathematica Scientia ,数学物理学报(英文版) , 编辑部邮箱 ,2009年01期

【分类号】O177
【下载频次】37

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