Articles

REMARKS ON JOHN DISKS

  • Chu Yuming ,
  • Cheng Jinfa ,
  • Wang Gendi
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  • Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China

Received date: 2006-10-20

  Revised date: 1900-01-01

  Online published: 2009-02-20

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 : R2R2 is a quasiconformal mapping if and only if f(D) is a John disk for any John disk D R2; 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.

Cite this article

Chu Yuming , Cheng Jinfa , Wang Gendi . REMARKS ON JOHN DISKS[J]. Acta mathematica scientia, Series B, 2009 , 29(1) : 160 -168 . DOI: 10.1016/S0252-9602(09)60016-3

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