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.
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.
