The Arc Distortion in QH Inner ψ-uniform （or Convex） Domains in Real Banach Spaces  

作　　者：Man Zi HUANG Xian Tao WANG 

机构地区：[1]Department of Mathematics, Hu'nan Normal University, Changsha 410081, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2011年第10期2039-2050,共12页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China （Grant No. 11071063）, Tianyuan Foundation （Grant No. 10926068） and Scientific Research Fund of Hunan Provincial Education Department （Grant No. 09C635）Acknowledgements The authors thank the referee very much for his （or her） careflfl reading of this paper and many useful suggestions and the support of the Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hu＇nan Province.

摘　　要：Let D and D＇ be domains in real Banach spaces of dimension at least 2. The main aim of this paper is to study certain arc distortion properties in the quasihyperbolic metric defined in real Banach spaces. In particular, when D＇ is a QH inner C-uniform domain with C being a slow （or a convex domain）, we investigate the following： For positive constants c, h, C, M, suppose a homeomorphism f ： D → D＇ takes each of the 10-neargeodesics in D to （c, h）-solid in D＇. Then f is C-coarsely M- Lipschitz in the quasihyperbolic metric. These are generalizations of the corresponding result obtained recently by Viiisiilg.Let D and D＇ be domains in real Banach spaces of dimension at least 2. The main aim of this paper is to study certain arc distortion properties in the quasihyperbolic metric defined in real Banach spaces. In particular, when D＇ is a QH inner C-uniform domain with C being a slow （or a convex domain）, we investigate the following： For positive constants c, h, C, M, suppose a homeomorphism f ： D → D＇ takes each of the 10-neargeodesics in D to （c, h）-solid in D＇. Then f is C-coarsely M- Lipschitz in the quasihyperbolic metric. These are generalizations of the corresponding result obtained recently by Viiisiilg.

关 键 词：Uniform domain QH C-uniform domain inner uniform domain QH inner C-uniform domain convex domain quasihyperbolic geodesic neargeodesic QUASICONVEXITY real Banach space 

分 类 号：TP393[自动化与计算机技术—计算机应用技术] O177.91[自动化与计算机技术—计算机科学与技术]