Quasihyperbolic metric and Quasisymmetric mappings in metric spaces
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- by Xiaojun Huang and Jinsong Liu PDF
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Abstract:
In this paper, we prove that the quasihyperbolic metrics are quasi-invariant under a quasisymmetric mapping between two suitable metric spaces. Meanwhile, we also show that quasi-invariance of the quasihyperbolic metrics implies that the corresponding map is quasiconformal. At the end of this paper, as an application of these theorems, we prove that the composition of two quasisymmetric mappings in metric spaces is a quasiconformal mapping.References
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Additional Information
- Xiaojun Huang
- Affiliation: College of Mathematics and Statistics, Chongqing University, Chongqing 401331, People’s Republic of China – and – Mathematical Sciences Research Institute in Chongqing, Chongqing 401331, People’s Republic of China
- Email: hxj@cqu.edu.cn
- Jinsong Liu
- Affiliation: HUA Loo-Keng Key Laboratory of Mathematics, Chinese Academic of Sciences, Beijing 100190, People’s Republic of China – and – Institute of Mathematics, Academic of Mathematics $\&$ System Sciences, Chinese Academic of Sciences, Beijing 100190, People’s Republic of China
- MR Author ID: 692700
- Email: liujsong@math.ac.cn
- Received by editor(s): June 13, 2012
- Received by editor(s) in revised form: January 21, 2013, April 27, 2013, and June 7, 2013
- Published electronically: February 19, 2015
- Additional Notes: The first author was supported by NSF of China (No. 11471318) and Natural Science Foundation Project of Chongqing (No. CSTC, 2011BB0055)
The second author was supported by NSFC Grant No. 11471318. - © Copyright 2015
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 367 (2015), 6225-6246
- MSC (2010): Primary 30C65
- DOI: https://doi.org/10.1090/S0002-9947-2015-06240-0
- MathSciNet review: 3356935