Quasiconformality to quasisymmetry via weak \((L,M)\)-quasisymmetry. (English) Zbl 1523.30032
Summary: This paper is devoted to the study of a fundamental problem in the theory of quasiconformal analysis: under what conditions local quasiconformality of a homeomorphism implies its global quasisymmetry. In particular, we introduce the concept of weak \((L,M)\)-quasisymmetry, serving as a bridge between local quasiconformality and global quasisymmetry. We show that in general metric spaces local regularity and some connectivity together with the Loewner condition are sufficient for a quasiconformal map to be weakly \((L,M)\)-quasisymmetric, and subsequently, quasisymmetric with respect to the internal metrics.
MSC:
| 30C65 | Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations |
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| [32] | Received 14 February 2022 • Revised received 2 September 2022 • Accepted 7 September 2022 Published online 18 September 2022 |
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