Acta mathematica scientia, Series B >
REMARKS ON JOHN DISKS
Received date: 2006-10-20
Revised date: 1900-01-01
Online published: 2009-02-20
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 : R2→ R2 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.
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
/
| 〈 |
|
〉 |