Quasiconformality to quasisymmetry via weak (L,M)-quasisymmetry
Keywords:Quasiconformal homeomorphism, quasisymmetric homeomorphism, Loewner space, LLC
AbstractThis 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
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