Geodesic
Quasiconformality to quasisymmetry via weak (L,M)-quasisymmetry
Tao Cheng1 ; Shanshuang Yang2
1 East China Normal University, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Department of Mathematics
2 Emory University, Department of Mathematics
Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 1131-1157.

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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.  
DOI : 10.54330/afm.121833
Keywords: Quasiconformal homeomorphism, quasisymmetric homeomorphism, Loewner space, LLC

Tao Cheng 1 ; Shanshuang Yang 2

1 East China Normal University, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Department of Mathematics
2 Emory University, Department of Mathematics 
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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. http://geodesic.mathdoc.fr/articles/10.54330/afm.121833/

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