1East China Normal University, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Department of Mathematics 2Emory University, Department of Mathematics
Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 1131-1157
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.
1
East China Normal University, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Department of Mathematics
2
Emory University, Department of Mathematics
Tao Cheng; Shanshuang Yang. Quasiconformality to quasisymmetry via weak (L,M)-quasisymmetry. Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 1131-1157. doi: 10.54330/afm.121833
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