Quasiconformality to quasisymmetry via weak (L,M)-quasisymmetry


  • Tao Cheng East China Normal University, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Department of Mathematics
  • Shanshuang Yang Emory University, Department of Mathematics


Quasiconformal homeomorphism, quasisymmetric homeomorphism, Loewner space, LLC


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.





How to Cite

Cheng, T., & Yang, S. (2022). Quasiconformality to quasisymmetry via weak (L,M)-quasisymmetry. Annales Fennici Mathematici, 47(2), 1131–1157. https://doi.org/10.54330/afm.121833