Free distance ratio mappings in Banach spaces

  • Qingshan Zhou
  • Antti Rasila
  • Yaxiang LiEmail author


In this paper, we introduce a class of mappings related to the distance ratio metric and study its connection to the freely quasiconformal mapping in Banach spaces. Moreover, we investigate the invariance of Gromov hyperbolic, natural and uniform domains under this class of mappings.


Quasihyperbolic metric Distance ratio metric Free distance ratio mapping Free quasiconformal mapping Uniform domains 

Mathematics Subject Classification

Primary 30C65 30F45 Secondary 30C20 



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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and Big DataFoshan UniversityFoshanPeople’s Republic of China
  2. 2.Guangdong TechnionIsrael Institute of TechnologyShantouPeople’s Republic of China
  3. 3.Department of MathematicsHunan First Normal UniversityChangshaPeople’s Republic of China
  4. 4.Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in EngineeringChangsha University of Science and TechnologyChangshaPeople’s Republic of China

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