Acta mathematica scientia,Series A

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Uniform Domain and Max-min Inequality Property

1,2Liao Maoxin; 3Chu Yuming; 4Li Xianyi   

  1. (1.Department of Mathematics, Central South University, Changsha 410083;
    2.School of Mathematics and Physics, Nanhua University, Hunan Henyang 421001; 3.Department of Mathematics, Huzhou University, Zhejiang Huzhou 313000; 4.Department of Mathematics, Shenzhen University, Guangdong Shenzhen 518060$)
  • Received:2007-04-30 Revised:2008-07-03 Online:2009-02-25 Published:2009-02-25
  • Contact: Liao Maoxin

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Abstract:

Introducing the max-min inequality property of domain,we investigate the relation between uniform domain and max-min inequality property, and obtain the following results: (1) if D is uniform domain, then D has max-min inequality property; (2) if D R2 and D*=R2\D have max-min inequality poperty, respectively, then D is uniform domain.

Key words: Uniform domain, Max-min inequality property, Weakly Cigar domain, Quasiconformal mappings, Quasi-invariance, Hyperbolic geodesic.

CLC Number: 

  • 30C60
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