数学物理学报(英文版)

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REMARKS ON JOHN DISKS

楮玉明;程金发;王根娣   

  1. Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China
  • 收稿日期:2006-10-20 修回日期:1900-01-01 出版日期:2009-02-20 发布日期:2009-02-20
  • 通讯作者: 楮玉明
  • 基金资助:

    Sponsored by the Foundation of Pre-973 Program of China under grant
    2006CB708304, the National NSFC under grant 10771195, and the NSF of Zhejiang Province under grant Y607128

REMARKS ON JOHN DISKS

Chu Yuming; Cheng Jinfa; Wang Gendi   

  1. Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China
  • Received:2006-10-20 Revised:1900-01-01 Online:2009-02-20 Published:2009-02-20
  • Contact: Chu Yuming

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 : 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.

关键词: John disks, Linearly locally connected domains, Quasiconformal mappings,
Quasidisks

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.

Key words: John disks, Linearly locally connected domains, Quasiconformal mappings,
Quasidisks

中图分类号: 

  • 30C62